To find the radius of the cone, we first need to calculate the volume of both the sphere and the cone.
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
So, the volume of the sphere with a radius of 6 cm is:
V_sphere = (4/3)π(6)^3 = 288π cm^3
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the cone and h is the height.
We are given that the height of the cone is 6 cm.
So, using the given volume, we can write:
288π = (1/3)π(r^2)(6)
864 = r^2(6)
r^2 = 144
r = 12
Therefore, the radius of the cone is 12 cm.
A sphere with a radius of 6 cm has the same volume as a cone with a height of 6 cm. What is the radius of the cone?
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