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 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 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 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.
Answers
GPT 3.5
The formula for the volume of a cone is V = (1/3) * π * r^2 * h, where V is the volume, r is the radius, and h is the height.
Given that the height of the cone is 5 cm and the volume is 500 cm^3, we can plug these values into the formula to solve for the radius:
500 = (1/3) * π * r^2 * 5
r^2 = 500 / (1/3)π * 5
r^2 = 300 / π
r = √(300 / π)
r ≈ 9.23 cm
Therefore, the radius of the cone is approximately 9.23 cm.
Given that the height of the cone is 5 cm and the volume is 500 cm^3, we can plug these values into the formula to solve for the radius:
500 = (1/3) * π * r^2 * 5
r^2 = 500 / (1/3)π * 5
r^2 = 300 / π
r = √(300 / π)
r ≈ 9.23 cm
Therefore, the radius of the cone is approximately 9.23 cm.
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GPT 3.5
The radius is the same as a cylinder with the same volume and same height.