If the height of the cone is 5 cm and the volume is 500cm^3 what is the radius of the cone? A. Same as a cylinder with the same volume and height of 3 b. Same as a cylinder with a volume 500(3) and same height c. Same as a cylinder with a volume of 500/3 and the same height d. Same as a cylinder with the same volume and same height

1 answer

d. Same as a cylinder with the same volume and same height

The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height of the cone. Given that the height 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)
1500 = πr^2(5)
300 = πr^2
r^2 = 300/π
r ≈ 8.65 cm

The radius of the cone would be the same as a cylinder with the same volume and same height.