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 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. 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.
Answers
GPT 3.5
To find the radius of the cone, we can use the formula for the volume of a cone which is V = (1/3)πr^2h, 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 have:
500 = (1/3)πr^2(5)
500 = (5/3)πr^2
r^2 = 500/(5/3)π
r^2 = 300/π
r = √(300/π)
Therefore, the radius of the cone is approximately equal to √(300/π) cm.
Given that the height of the cone is 5 cm and the volume is 500 cm^3, we have:
500 = (1/3)πr^2(5)
500 = (5/3)πr^2
r^2 = 500/(5/3)π
r^2 = 300/π
r = √(300/π)
Therefore, the radius of the cone is approximately equal to √(300/π) cm.