he volume of a sphere is 48 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?
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. We are given that the volume of the sphere is 48 m^3, so we can set up an equation:
48 = (4/3)πr^3
To find the volume of a cylinder with the same radius as the sphere and a height equal to the sphere's diameter (which is twice the radius), we can use the formula V = πr^2h, where r is the radius and h is the height. Since the height of the cylinder is equal to 2r, we have:
V = πr^2(2r)
= 2πr^3
Using the equation we found earlier to determine the value of r, we can substitute it into the equation for the volume of the cylinder:
V = 2πr^3
= 2π((3/4)(48/π))^(1/3)
= 2π(36/4)^(1/3)
= 2π(9)^(1/3)
=~ 40.84 m^3
Therefore, the volume of the cylinder is approximately 40.84 cubic meters.