{"id":72,"date":"2026-08-05T06:26:27","date_gmt":"2026-08-05T06:26:27","guid":{"rendered":"https:\/\/sqoolpapers.co.za\/notes\/measurement-g12-maths-t4p2\/"},"modified":"2026-08-22T16:24:47","modified_gmt":"2026-08-22T16:24:47","slug":"measurement-g12-maths-t4p2","status":"publish","type":"post","link":"https:\/\/repstaq.com\/study-guide-docs\/measurement-g12-maths-t4p2\/","title":{"rendered":"Measurement-G12-Maths-T4P2"},"content":{"rendered":"\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Measurement<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Measurement deals with length, perimeter, area, surface area, volume and capacity. In examination questions, learners must select the correct formula, use consistent units, substitute accurately and round only the final answer. Diagrams are not always drawn to scale, so use the given measurements rather than estimating from the drawing.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Two dimensional measurement<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Two dimensional measurement concerns flat figures. Length is measured in units such as millimetres, centimetres and metres. Perimeter is measured in linear units, while area is measured in square units.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Important formulas<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rectangle:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nP=2(l+w)\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nA=lw\n<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Triangle:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nA=\\frac{1}{2}bh\n<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Parallelogram:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nA=bh\n<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Trapezium:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nA=\\frac{1}{2}(a+b)h\n<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Circle:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nC=2\\pi r\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nA=\\pi r^2\n<\/span><\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Remember<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The perpendicular height must be used in an area formula.<\/li>\n\n\n\n<li>The radius is half the diameter.<\/li>\n\n\n\n<li>Convert all measurements to the same unit before calculating.<\/li>\n<\/ul>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Question: A trapezium has parallel sides of length <span class=\"katex-eq\" data-katex-display=\"false\">8\\text{ cm}<\/span> and <span class=\"katex-eq\" data-katex-display=\"false\">14\\text{ cm}<\/span>. Its perpendicular height is <span class=\"katex-eq\" data-katex-display=\"false\">6\\text{ cm}<\/span>. Calculate its area.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Identify the given information.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\na=8\\text{ cm},\\quad b=14\\text{ cm},\\quad h=6\\text{ cm}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Write the formula.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nA=\\frac{1}{2}(a+b)h\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 3: Substitute the values.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nA=\\frac{1}{2}(8+14)(6)\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 4: Simplify.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nA=\\frac{1}{2}(22)(6)\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nA=66\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 5: State the final answer.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nA=66\\text{ cm}^2\n<\/span><\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Common Mistake<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Do not add all the side lengths when area is required. Adding side lengths gives the perimeter.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Exam Tip<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A complete examination solution should show the required length, the correct area formula, substitution and the final answer with square units. This step-by-step approach is reflected in the allocation of marks for area calculations.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Three dimensional measurement<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Three dimensional objects have length, width and height. They occupy space and may have flat faces, curved surfaces, edges and vertices.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Important facts<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A prism has a constant cross-section throughout its length.<\/li>\n\n\n\n<li>A cylinder has two congruent circular bases.<\/li>\n\n\n\n<li>A pyramid has one base and triangular faces meeting at an apex.<\/li>\n\n\n\n<li>A cone has a circular base and a curved surface meeting at an apex.<\/li>\n\n\n\n<li>A sphere has one continuous curved surface.<\/li>\n\n\n\n<li>The perpendicular height is used for volume.<\/li>\n\n\n\n<li>The slant height of a cone or pyramid may be needed for surface area.<\/li>\n<\/ul>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Question: A cone has a perpendicular height of <span class=\"katex-eq\" data-katex-display=\"false\">12\\text{ cm}<\/span> and a radius of <span class=\"katex-eq\" data-katex-display=\"false\">5\\text{ cm}<\/span>. Calculate its slant height.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Identify the given information.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nh=12\\text{ cm},\\quad r=5\\text{ cm}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Apply the theorem of Pythagoras.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\ns^2=h^2+r^2\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 3: Substitute the values.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\ns^2=12^2+5^2\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 4: Simplify.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\ns^2=144+25\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\ns^2=169\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\ns=\\sqrt{169}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 5: State the final answer.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\ns=13\\text{ cm}\n<\/span><\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Common Mistake<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Do not use the slant height in the volume formula. Volume always uses the perpendicular height.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/sqooltutors.co.za\/sign-up-b\/\"><img decoding=\"async\" src=\"https:\/\/lmxddlwowqlsyucleuyv.supabase.co\/storage\/v1\/object\/public\/pdf_ads\/batch%201\/Doc%20Image%20Aug%2022,%202026,%2004_22_25%20PM%20(1).png\" alt=\"\"\/><\/a><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Surface area<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Surface area is the total area of all the outside surfaces of a three-dimensional object. A net can help identify every face that must be included.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Important formulas<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rectangular prism:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nSA=2(lw+lh+wh)\n<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Closed cylinder:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nSA=2\\pi r^2+2\\pi rh\n<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Closed cone:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nSA=\\pi r^2+\\pi rs\n<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sphere:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nSA=4\\pi r^2\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For an open container, exclude the missing face or base.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Question: Calculate the total surface area of a closed cylinder with radius <span class=\"katex-eq\" data-katex-display=\"false\">3\\text{ cm}<\/span> and height <span class=\"katex-eq\" data-katex-display=\"false\">10\\text{ cm}<\/span>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Identify the given information.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nr=3\\text{ cm},\\quad h=10\\text{ cm}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Write the formula.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nSA=2\\pi r^2+2\\pi rh\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 3: Substitute the values.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nSA=2\\pi(3)^2+2\\pi(3)(10)\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 4: Simplify.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nSA=18\\pi+60\\pi\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nSA=78\\pi\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nSA\\approx245{,}04\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 5: State the final answer.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nSA\\approx245{,}04\\text{ cm}^2\n<\/span><\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Common Mistake<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Forgetting one or both circular ends of a closed cylinder leads to an incomplete surface area.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Volume<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Volume measures the amount of space inside a three-dimensional object. It is measured in cubic units. Capacity is commonly measured in millilitres or litres.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Important conversions<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n1\\text{ cm}^3=1\\text{ mL}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n1\\,000\\text{ cm}^3=1\\text{ L}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n1\\text{ m}^3=1\\,000\\text{ L}\n<\/span><\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Important formulas<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Prism:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV=A_{\\text{base}}h\n<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cylinder:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV=\\pi r^2h\n<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Pyramid:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV=\\frac{1}{3}A_{\\text{base}}h\n<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cone:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV=\\frac{1}{3}\\pi r^2h\n<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sphere:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV=\\frac{4}{3}\\pi r^3\n<\/span><\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Question: Calculate the volume of a sphere with radius <span class=\"katex-eq\" data-katex-display=\"false\">6\\text{ cm}<\/span>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Identify the given information.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nr=6\\text{ cm}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Write the formula.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV=\\frac{4}{3}\\pi r^3\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 3: Substitute the value.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV=\\frac{4}{3}\\pi(6)^3\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 4: Simplify.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV=\\frac{4}{3}\\pi(216)\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV=288\\pi\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV\\approx904{,}78\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 5: State the final answer.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV\\approx904{,}78\\text{ cm}^3\n<\/span><\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Exam Tip<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Keep the value involving pi on the calculator and round only the final answer. Do not assume missing measurements, because assumed values are not accepted in examination solutions.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Composite solids<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A composite solid consists of two or more basic solids joined together or with one solid removed from another. Break the object into familiar parts before calculating.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Method<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Identify each basic solid.<\/li>\n\n\n\n<li>Decide whether volumes must be added or subtracted.<\/li>\n\n\n\n<li>Identify any shared surfaces that must not be included in surface area.<\/li>\n\n\n\n<li>Write a separate formula for each part.<\/li>\n\n\n\n<li>Use consistent units.<\/li>\n<\/ul>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Question: A solid consists of a cylinder with a hemisphere attached to its top. Both parts have radius <span class=\"katex-eq\" data-katex-display=\"false\">3\\text{ cm}<\/span>. The cylinder has height <span class=\"katex-eq\" data-katex-display=\"false\">8\\text{ cm}<\/span>. Calculate the total volume.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Write the volume of the cylinder.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV_{\\text{cylinder}}=\\pi r^2h\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Substitute the values.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV_{\\text{cylinder}}=\\pi(3)^2(8)\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV_{\\text{cylinder}}=72\\pi\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 3: Write the volume of the hemisphere.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV_{\\text{hemisphere}}=\\frac{1}{2}\\left(\\frac{4}{3}\\pi r^3\\right)\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 4: Substitute the radius.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV_{\\text{hemisphere}}=\\frac{2}{3}\\pi(3)^3\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV_{\\text{hemisphere}}=18\\pi\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 5: Add the volumes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV_{\\text{total}}=72\\pi+18\\pi\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV_{\\text{total}}=90\\pi\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV_{\\text{total}}\\approx282{,}74\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 6: State the final answer.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV_{\\text{total}}\\approx282{,}74\\text{ cm}^3\n<\/span><\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Common Mistake<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">When calculating the surface area of joined solids, do not include the circular surface where the cylinder and hemisphere meet because it is inside the solid.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/sqooltutors.co.za\/sign-up-b\/\"><img decoding=\"async\" src=\"https:\/\/lmxddlwowqlsyucleuyv.supabase.co\/storage\/v1\/object\/public\/pdf_ads\/batch%201\/Doc%20Image%20Aug%2022,%202026,%2004_21_14%20PM%20(1).png\" alt=\"\"\/><\/a><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Applications involving prisms, cylinders, cones, pyramids and spheres<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Measurement is used in construction, packaging, storage, transport, manufacturing and design.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Prisms<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Prisms model objects such as boxes, buildings, swimming pools and channels. Their volume is the area of the constant cross-section multiplied by the length.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Cylinders<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Cylinders model tanks, pipes, cans and silos. Questions may involve capacity, material cost or the rate at which a tank fills.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Cones<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Cones model funnels, tents and conical containers. Read carefully whether the perpendicular height or slant height is required.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Pyramids<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Pyramids appear in roof structures, ornaments and packaging. The area of the base depends on whether the base is a square, rectangle or another polygon.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Spheres<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Spheres model balls, globes and spherical tanks. A hemisphere is half a sphere.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Question: A cylindrical water tank has radius <span class=\"katex-eq\" data-katex-display=\"false\">1{,}5\\text{ m}<\/span> and height <span class=\"katex-eq\" data-katex-display=\"false\">2\\text{ m}<\/span>. Calculate its capacity in litres.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Identify the given information.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nr=1{,}5\\text{ m},\\quad h=2\\text{ m}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Write the formula.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV=\\pi r^2h\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 3: Substitute the values.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV=\\pi(1{,}5)^2(2)\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 4: Simplify.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV=4{,}5\\pi\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nV\\approx14{,}137\\text{ m}^3\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 5: Convert to litres.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n14{,}137\\times1\\,000=14\\,137\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 6: State the final answer.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\text{Capacity}\\approx14\\,137\\text{ L}\n<\/span><\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Exam Tip<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw and label a simplified diagram.<\/li>\n\n\n\n<li>Distinguish between radius and diameter.<\/li>\n\n\n\n<li>Check whether the object is open or closed.<\/li>\n\n\n\n<li>Use square units for area and cubic units for volume.<\/li>\n\n\n\n<li>Show all formulas and substitutions.<\/li>\n\n\n\n<li>Do not round intermediate answers.<\/li>\n\n\n\n<li>Check whether the final answer is reasonable in the given context.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Measurement Measurement deals with length, perimeter, area, surface area, volume and capacity. In examination questions, learners must select the correct formula, use consistent units, substitute accurately and round only the final answer. Diagrams are not always drawn to scale, so use the given measurements rather than estimating from the drawing. Two dimensional measurement Two dimensional [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_breakdance_hide_in_design_set":false,"_breakdance_tags":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-72","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"acf":{"document_name":"Measurement","grade":12,"subject":"Mathematics","term":4,"paper":2},"_links":{"self":[{"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/posts\/72","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/comments?post=72"}],"version-history":[{"count":2,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/posts\/72\/revisions"}],"predecessor-version":[{"id":228,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/posts\/72\/revisions\/228"}],"wp:attachment":[{"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/media?parent=72"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/categories?post=72"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/tags?post=72"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}