The surface area of a spherical balloon measured in square inches is the same as its volume, measured in cubic inches. What is the diameter of the balloon?
Answer: 6 inches. The surface area of a sphere, of radius r, is 4 * Pi * (r ^ 2) and the volume is (4/3) * Pi * (r^3). Putting these equal and cancelling gives r = 3, which means the diameter is 6 inches. QED.
My bath has two taps and a plug hole.
The cold tap on its own fills the bath in 12 minutes, the hot one in 8 minutes.
The plug hole can drain the bath in 24 minutes with the taps off.
How long will the bath take to fill if I leave both taps on with the plug left out?