Determine the volume of the sphere with given surface area

What is the volume of the sphere with a surface area of 144π?

Hint: Use the surface area formula to find the radius of the sphere first.

Volume of the sphere:

To find the volume of the sphere, we need to find its radius using the surface area formula. Once we have the radius, we can use the volume formula to calculate the volume of the sphere.

The surface area of a sphere is given as 144π. We can start by using the formula for the surface area of a sphere, which is 4πr², where r is the radius of the sphere.

Given that the surface area of the sphere is 144π, we can set up the equation: 4πr² = 144π. Dividing both sides by 4π, we get r² = 36. Taking the square root of both sides, the radius of the sphere is found to be 6.

Now that we have the radius, we can calculate the volume of the sphere using the formula V = (4/3)πr³. By substituting the value of the radius (6), we can calculate the volume of the sphere as 288π cubic units.