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 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 volume of a cone is V = (1/3)πr^2h, where 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 substitute these values into the formula and solve for the radius:
500 = (1/3)πr^2(5)
r^2 = 500 * (3/π) * (1/5)
r^2 = 300
r = √300
r ≈ 17.32
Therefore, the radius of the cone is approximately 17.32 cm.