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 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. The radius is the same as a cylinder with the same volume and same height.
The volume of a cone is given by V = (1/3)πr^2h, where r is the radius and h is the height.
Given that the volume of the cone is 500 cm^3 and the height is 5 cm, we have:
500 = (1/3)πr^2(5)
Solving for r:
500 = (5/3)πr^2
r^2 = 500 / (5/3)π
r^2 = 300 / π
r ≈ √(300 / π)
r ≈ √(300) / √(π)
r ≈ 17.32 / 3.14
r ≈ 5.5 cm
Therefore, the radius of the cone is approximately 5.5 cm.