The volume of a sphere is 185π cm3. What is the volume of a cylinder 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 is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
Given that the volume of the sphere is 185π cm^3, we can equate this to the formula and solve for r:
185π = (4/3)πr^3
Dividing both sides of the equation by π, we get:
185 = (4/3)r^3
Simplifying the equation further, we multiply both sides by 3/4:
(3/4) * 185 = (3/4) * (4/3)r^3
138.75 = r^3
To find the radius, we take the cube root of 138.75:
r = ∛138.75
r ≈ 5
The height of the cylinder is equal to the sphere's diameter, which is twice the radius of the sphere. Therefore, the height of the cylinder is 2r = 2 * 5 = 10 cm.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height of the cylinder.
Plugging in the values we found, the volume of the cylinder is:
V = π(5^2)(10)
V = 250π cm^3
Therefore, the volume of the cylinder is 250π cm^3.