Question

The volume of a sphere is 72 m^3. What is the volume of a cone if its radius is the

same as the sphere's and its height is equal to the sphere's diameter? (1 point)

Answer 1

Explanation:

the volume of a cone is

pi×r²×h/3

r being the radius, h bring the height.

the volume of a sphere is

pi×r³×4/3

r is the same number for both objects.

the diameter of the sphere (= height of the cone) is 2×r. it is the same principle as for a circle.

so the volume of our cone is simplified

pi×r²×(2r)/3 = pi×r³×2/3

when we compare both volumes

pi×r³×4/3

pi×r³×2/3

we see that the volume of the sphere is twice the volume of the cone.

therefore the volume of the cone is

72 / 2 = 36 m³