Find the volume of a sphere with a surface area of 2304 inches squared
(Type an exact answer in terms of pie.)
The formula for the surface area of a sphere is 4πr^2, where r is the radius of the sphere.
Given that the surface area is 2304 inches squared, we can set up the equation as follows:
4πr^2 = 2304
To find the volume, we can use the formula V = (4/3)πr^3.
First, let's solve for the radius (r). Divide both sides of the equation by 4π:
r^2 = 2304 / (4π)
r^2 = 576 / π
r = √(576 / π)
Now substitute the value of r into the volume formula:
V = (4/3)π(√(576/π))^3
V = (4/3)π(4/π)^3
V = (4/3)π(4^3/π^3)
V = 4(4^3/3π^2)
V = 256/3π^2 cubic inches
Therefore, the volume of the sphere with a surface area of 2304 inches squared is (256/3)π^2 cubic inches.