The volume of a sphere is 48 m^3. What is the volume of a cylinder if its radius is the same as the spheres and its height is equal to the spheres diameter?

1 answer

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where V is the volume and r is the radius.

Given that the volume of the sphere is 48 m^3, we can use the formula to find the radius:
48 = (4/3)πr^3

Simplifying the equation:
48*(3/4) = πr^3
36 = πr^3

Dividing both sides of the equation by π and taking the cube root:
(36/π)^(1/3) = r

The radius of the sphere is approximately 2.9086 meters.

The height of the cylinder is equal to the sphere's diameter, which is twice the radius:
Height = 2 * r = 2 * 2.9086 ≈ 5.8172 meters.

The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.

Plugging in the values:
V = π * 2.9086^2 * 5.8172 ≈ 100.4056 m^3.

Therefore, the volume of the cylinder is approximately 100.4056 m^3.