Maths · Mensuration. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Volume is the space inside a solid, measured in cubic units such as cm3. Surface area is the total area of all the outside faces, measured in square units such as cm2.
A prism has the same cross-section all the way along, so its volume is the area of the cross-section times the length. A cuboid and a cylinder both work this way. A pyramid or a cone comes to a point, and its volume is one third of base area times height.
For surface area, think of the net: list every face, find each area, then add. The curved surface of a cone uses the slant height l, not the vertical height h. Find l with l2 = r2 + h2.
Students forget to square the radius, or use the diameter where the formula needs the radius. Write the formula first, halve the diameter if you are given it, then substitute.
Answer: 204 cm2
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