Volume & surface area · SAT Maths

Concept

The formulas you need at your fingertips:

Rectangular prism — V = lwh · SA = 2(lw + lh + wh)
Cube — V = s³ · SA = 6s²
Cylinder — V = πr²h · lateral SA = 2πrh
Cone — V = (1/3)πr²h
Sphere — V = (4/3)πr³ · SA = 4πr²

Two memorisable relationships: a cone has one third the volume of a cylinder with the same base and height. A sphere's surface area is exactly four times the area of one of its great circles (πr² × 4).

Worked example 1

Find the volume of a cylinder with radius 3 and height 8.

Solution

Formula. V = πr²h

Plug in. V = π(3²)(8) = π · 9 · 8 = 72π

V = 72π ≈ 226.2 cubic units.

Worked example 2

A cone and a cylinder share the same radius (4) and height (6). Find both volumes and the ratio.

Solution

Cylinder. V_cyl = π(16)(6) = 96π

Cone. V_cone = (1/3)(96π) = 32π

Cone : Cylinder = 1 : 3. The cone holds exactly one-third the volume.

Practice test

8 questions on volumes and surface areas of common 3-D solids.

Practice test · 8 questions Question 1 of 8 · Score 0