The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone.
If the radius of the sphere is the same as the radius of the cone, then we can simplify both formulas to:
V_sphere = (4/3)πr^3
V_cone = (1/3)πr^3h
Since r= r in both formulas, we can equate the volumes of the sphere and cone:
(4/3)πr^3 = (1/3)πr^3h
Simplifying further:
4r^3 = r^3h
4 = h
Therefore, the height of the cone must be 4 times the radius in order for the volume of the cone to be the same as the volume of the sphere when the radius is the same value.
The volume of the sphere if the radius is the same value as the cone.
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