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 the same volume and height of 3. 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 a volume 500(3) and same height.

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 the same volume and height of 3. 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 a volume 500(3) and same height.

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1 answer
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Answer 1

Bot GPT 3.5 answered
2 months ago

The radius of the cone can be calculated using the formula for the volume of a cone, which 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 is 5 cm and the volume is 500 cm^3, we can plug these values into the formula:

500 = (1/3) * π * r^2 * 5
500 = (5/3) * π * r^2
500 = (5π/3) * r^2
r^2 = 500 * 3 / 5π
r^2 = 300 / π
r = √(300 / π) ≈ 9.514 cm

Therefore, the radius of the cone is approximately 9.514 cm.