The volume of a sphere is 60 cubic meters. Find the volume of a cylinder with the same dimensions. show work
The formula for the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius.
We are given that the volume of the sphere is 60 cubic meters, so 60 = (4/3)πr³.
To find the radius of the sphere, we can rearrange the equation to solve for r: r³ = (3/4)(60/π) = 45/π.
Taking the cube root of both sides, we get r ≈ 2.663.
Now, let's find the volume of a cylinder with the same dimensions.
The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
Since the sphere and the cylinder have the same dimensions, the height of the cylinder will be twice the radius of the sphere: h = 2(2.663) ≈ 5.326.
Plugging in the values, the volume of the cylinder is V = π(2.663)²(5.326) ≈ 72.190 cubic meters.
Therefore, the volume of the cylinder with the same dimensions is approximately 72.190 cubic meters.