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 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.
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 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.
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The radius can be calculated using the formula for the volume of a cone V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height. Plugging in the values given (V = 500 cm^3, h = 5 cm), we get 500 = (1/3)πr^2(5).
Solving for r, we get r^2 = (3 * 500) / (π * 5) = 300 / π.
Taking the square root of both sides, we get r ≈ √(300 / π) ≈ 7.02 cm.
Therefore, the radius of the cone is approximately 7.02 cm.