2018 · Q74
There are as many square centimetres in the surface area of a sphere as there are cubic centimetres in its volume. What is the radius of the sphere?
Elementary MathematicsMensuration
- A4 cm
- B3 cm
- C2 cm
- D1 cm
Explanation
The sphere's surface area is 4πr² and its volume is (4/3)πr³. Equating the numerical values: 4πr² = (4/3)πr³. Cancelling 4πr² from both sides (r ≠ 0) leaves 1 = r/3, so r = 3 cm. This is the well-known radius at which a sphere's surface-area number equals its volume number. Hence option (B) 3 cm.