The volume of a sphere is 36 m³. 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? (Round to the nearest whole number)
The volume of a sphere is given by the formula: V = (4/3) * π * r^3, where V is the volume and r is the radius of the sphere.
Given that the volume of the sphere is 36 m³, we can rearrange the equation to solve for the radius of the sphere:
36 = (4/3) * π * r^3
36 * 3/4π = r^3
(36 * 3/4π)^(1/3) = r
Using a calculator, we can find the approximate value of the radius of the sphere:
r ≈ 2.62 m
The height of the cylinder is equal to the diameter of the sphere, which is twice the radius:
height = 2 * radius
height ≈ 2 * 2.62
height ≈ 5.24 m
The formula for the volume of a cylinder is: V = π * r^2 * h, where V is the volume, r is the radius, and h is the height of the cylinder.
Substituting the values we found:
V = π * (2.62)^2 * 5.24
V ≈ π * 6.87 * 5.24
V ≈ 113.22
Rounding to the nearest whole number, the volume of the cylinder is approximately 113 m³.