The volume of a sphere is
72 m3. 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?
The volume of a sphere with radius r is given by the formula V = (4/3)πr^3.
Given that the volume of the sphere is 72 m^3, we can set up the equation:
72 = (4/3)πr^3
To find the radius:
72 * 3/4π = r^3
r^3 = 54π
Taking the cube root of both sides:
r ≈ 3.92 meters
The height of the cone is equal to the sphere's diameter, which is twice the radius:
height = 2 * r = 2 * 3.92 ≈ 7.84 meters
The volume of a cone with radius r and height h is given by the formula V = (1/3)πr^2h.
Substituting the values:
V = (1/3)π(3.92)^2(7.84) ≈ 193.3 m^3
Therefore, the volume of the cone is approximately 193.3 m^3.