Question

If the height of the cone is 5 cm and the volume is 500 cm^3, what is the radius of the cone?

(1 point)

The radius is the same as a cylinder with the same volume and height of 3.

The radius is the same as a cylinder with the same volume and same height.

The radius is the same as a cylinder with a volume of 500/3 and the same height.

The radius is the same as a cylinder with a volume 500(3) and same height.
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Answer 1

Volume of a cone: V = (1/3)πr^2h. So r^2 = 3V/(πh).

With V = 500 and h = 5: r^2 = 3·500/(π·5) = 300/π, so r = sqrt(300/π) ≈ 9.77 cm.

This matches a cylinder of the same height whose volume is 3·500 = 1500 cm^3. (Option 4.)