identify the volume and surface area of a sphere in terms of pi with a great circle area of 144 pi ft

Volume of sphere is 2,304 pi ft^3

Surface area of sphere is 576 pi ft^2

Step-by-step explanation:

When we talk of a great circle, we are talking of a circle around the sphere that has the same radius as the sphere.

Mathematically the area of the great circle is pi * r * r

now pi * r^2 = 144 pi

divide both sides by pi

r^2 = 144

r^2 = 12^2

since power are equal, we equate bases and the radius of the circle is thus equal to 12 feet

Now to calculate the volume of the sphere,

We know that the volume of a sphere is;

V = 4/3 * pi * r^3

V = 4/3 * pi * 12^3

V = 4 * pi * 4 * 12^2 = 2304 pi ft^3

The surface area of the sphere is mathematically equal to 4 * pi * r^2

= 4 * pi * 12^2 = 576 pi ft^2