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)
Responses

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 of 500/3 and the same height.

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

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

The radius can be calculated using the formula for the volume of a cone, which is (1/3) * π * r^2 * h, where r is the radius and h is the height.

Given that the height is 5 cm and the volume is 500 cm^3, we can plug these values into the formula and solve for the radius:

500 = (1/3) * π * r^2 * 5
r^2 = 500 * 3 / (π * 5)
r^2 = 300 / π
r ≈ √(300 / π)

Therefore, the radius of the cone is approximately equal to the square root of 300 divided by π, which is approximately 7.74 cm.