The volume of a sphere is 48m ^ 3 What is the volume of a cylinder if its radius is the same as the sphere's and height is equal to the sphere's diameter? (1 point)
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.
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 radius of the cylinder is the same as the sphere's radius, and the height of the cylinder is equal to the sphere's diameter (which is twice the radius), we can substitute these values into the formula for the volume of a cylinder:
V = πr^2h
= πr^2(2r)
= 2πr^3
Given that the volume of the sphere is 48m^3, we can substitute this value into the formula for the volume of the sphere:
48 = (4/3)πr^3
To find the radius (r), we can rearrange this equation:
r^3 = (3/4) * 48 / π
r^3 = 36 / π
r = (36 / π)^(1/3)
Now we can substitute the value of r into the formula for the volume of the cylinder:
V = 2πr^3
= 2π * ((36 / π)^(1/3))^3
= 2π * (36 / π)
= 72
Therefore, the volume of the cylinder is 72m^3.