Volume of sphere is 60 cubic meter. Find volume of cylinder with same dimensions
To find the volume of the cylinder with the same dimensions as the sphere, we need to determine the radius of the sphere.
The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.
Given that the volume of the sphere is 60 cubic meters, we can equate this to the formula:
60 = (4/3)πr^3
To find r, we divide both sides of the equation by (4/3)π:
60 / (4/3)π = r^3
Simplifying, we get:
45π = r^3
To find the radius r, we take the cube root of both sides:
r = (45π)^(1/3)
Once we have the radius of the sphere, we can use it to find the volume of the cylinder.
The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
Since the dimensions of the cylinder are the same as the sphere, the height of the cylinder will also be (45π)^(1/3).
The volume of the cylinder is then:
V = πr^2h
= π((45π)^(1/3))^2((45π)^(1/3))
= π((45π)^(2/3))((45π)^(1/3))
= π(45π)^(2/3 + 1/3)
= π(45π)^(3/3)
= π(45π)
So the volume of the cylinder with the same dimensions as the sphere is 45π cubic meters.