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 of 500/3 and the 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 same height.
The radius is the same as a cylinder with the same volume and height of 3.
is that correct
My apologies for the error in the response. Let's correct that:
To find the radius of a cone, you 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, h is the height of the cone. Given that the height is 5 cm and the volume is 500 cm^3:
500 = (1/3) x π x r^2 x 5
500 = (5/3) x π x r^2
r^2 = (3 x 500)/(5 x π)
r^2 = 300/π
r ≈ √(300/π)
r ≈ 7.74 cm
Therefore, the radius of the cone is approximately 7.74 cm.