Volume & Surface Area Questions with Solutions

This topic covers the mensuration of three-dimensional solids: cubes, cuboids, cylinders, cones, spheres, hemispheres and frustums. You need to know the formulas for the volume, curved surface area and total surface area of each solid. For example, the volume of a cylinder is pi r^2 h and the volume of a sphere is (4/3) pi r^3. Exam questions test direct use of the formulas, melting one solid and recasting it into others (the volume stays the same), the number of small solids that can be made from a larger one, the effect of changing dimensions, water flowing through a pipe into a tank, and the cost of painting or covering a surface. When every length of a solid is multiplied by k, its surface area is multiplied by k^2 and its volume by k^3. This fact solves many questions about changing dimensions in a single step. Practise the volume and surface area questions below, each with a step-by-step solution.