A right-angled triangle with legs 3 cm and 4 cm is spun once about its 4 cm leg, and then spun instead about its 3 cm leg. Find the ratio of the volume of the first cone to the volume of the second.

Spinning about the 4 cm leg gives a cone of radius 3 cm and height 4 cm: (1/3)π × $9\times 4=12$π ${\text{cm}}^3$. Spinning about the 3 cm leg gives radius 4 cm and height 3 cm: (1/3)π × $16\times 3=16$π ${\text{cm}}^3$. Ratio = 12 : 16 = 3 : 4. (The radius is squared but the height is not, so the fatter cone holds more — the answer is not 4 : 3, and the squares 9 : 16 ignore the heights.)