Question

If the cylinder and the cone shown have the same volume, then the radius and height of the cone could be which of these?

(2 points)

radius of the cone = 5; height of the cone = 12

radius of the cone = 5; height of the cone = 4

radius of the cone = 15; height of the cone = 4

radius of the cone = 15; height of the cone = 12
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Answer 1

Volume condition: (1/3)πr^2h = πR^2H, so r^2h = 3R^2H.

If the cylinder is radius 5 and height 12, R^2H = 25·12 = 300, so r^2h = 900.

Check choices:
- 5,12: 25·12 = 300
- 5,4: 25·4 = 100
- 15,4: 225·4 = 900 ← matches
- 15,12: 225·12 = 2700

Thus radius = 15 and height = 4.