The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
Let's solve for r in the given equation for the volume of the sphere:
18/(5π) = (4/3)πr^3
r^3 = (3/4) * (18/(5π))
r^3 = 27/(10π)
r = (27/(10π))^(1/3)
Now, the height of the cylinder is equal to the diameter of the sphere, which is 2r. So, the height of the cylinder is 2 * (27/(10π))^(1/3).
The volume of the cylinder is given by the formula V = πr^2h, where r is the radius of the cylinder and h is its height.
Substituting the values, the volume of the cylinder is π[(27/(10π))^(1/3)]^2 * 2 * (27/(10π))^(1/3), which simplifies to π[(27^2 * 2)/ (100π^2)]^(1/3) * 2 * [(27/(10π))^(1/3)], which further simplifies to (54/100) * (27/(10π))^(1/3).
Thus, the volume of the cylinder is approximately (54/100) * (27/(10π))^(1/3) cm^3.
The volume of a sphere is 18 divided by 5π 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?
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