This article covers the essential skills of surface area and volume of 3D solids – a core topic in DSE Paper 1 Section A(2) and Section B worth 4–6 marks. You will learn the formulas for volume and surface area of common solids: prisms, cylinders, cones, spheres, and pyramids. You will also learn the length, area, and volume ratios for similar solids, and how to solve problems involving composite solids. The article includes step-by-step worked examples, DSE exam techniques, practice questions. These are essential skills that appear regularly in DSE papers.
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Mensuration | Surface Area & Volume of 3D Solids
Question 1 MC
Find the volume of a sphere with radius 6 cm.
A. \( 144\pi \) B. \( 288\pi \) C. \( 432\pi \) D. \( 576\pi \)
Question 2 MC
A cylinder has radius 4 cm and height 7 cm. What is its total surface area?
A. \( 56\pi \) B. \( 88\pi \) C. \( 96\pi \) D. \( 112\pi \)
Question 3 Short Answer
A cone has radius 3 cm and height 4 cm. Find its volume.
Question 4 Short Answer
Two similar cones have surface areas \( 50\pi \) and \( 200\pi \). Find the ratio of their heights.
Question 5 MC
The volume of a sphere is \( 288\pi \) cm³. Find its radius.
A. \( 4 \) cm B. \( 5 \) cm C. \( 6 \) cm D. \( 8 \) cm
Question 6 Short Answer
A rectangular prism has dimensions 5 cm × 4 cm × 3 cm. Find its total surface area.
Question 7 MC
A cone and a cylinder have the same radius and height. The cone's volume is 36 cm³. What is the cylinder's volume?
A. \( 12 \) B. \( 36 \) C. \( 72 \) D. \( 108 \)
Question 8 Short Answer
A solid is made of a hemisphere of radius 5 cm on top of a cylinder of the same radius and height 8 cm. Find the total volume.
Question 9 Short Answer
Find the slant height of a cone with radius 6 cm and height 8 cm.
Question 10 Short Answer
Two similar solids have volumes \( 64 \) cm³ and \( 216 \) cm³. Find the ratio of their surface areas.
When calculating total surface area of a composite solid, remember to subtract the area of any faces that are hidden or internal. Only count the exposed surfaces.