A sphere has a surface area of 144\pi square inches. What is the volume, in cubic inches, … — SAT

A sphere has a surface area of $144\pi$ square inches. What is the volume, in cubic inches, of the sphere?

The volume of the sphere is

288\pi

cubic inches.

The surface area of a sphere is given by

A = 4\pi r^2

, where

r

is the radius. Setting this equal to the given surface area yields

4\pi r^2 = 144\pi

, which simplifies to

r^2 = 36

, meaning the radius of the sphere is

6

inches. The volume of a sphere is given by

V = \frac{4}{3}\pi r^3

. Substituting

r = 6

into this formula gives

V = \frac{4}{3}\pi (6^3) = \frac{4}{3}\pi (216) = 288\pi

cubic inches.

Set the formula for the surface area of a sphere,

A = 4\pi r^2

, equal to the given surface area of

144\pi

4\pi r^2 = 144\pi

, which simplifies to

r^2 = 36

To find the square of the radius of the sphere.

Take the square root of both sides to find the radius

r

r = 6

The radius of a sphere must be a positive number.

Substitute the radius

r = 6

into the formula for the volume of a sphere,

V = \frac{4}{3}\pi r^3

V = \frac{4}{3}\pi(6^3) = \frac{4}{3}\pi(216) = 288\pi

To compute the final volume of the sphere.

The volume of a sphere can be calculated by first finding its radius from its surface area using the formulas

A = 4\pi r^2

and

V = \frac{4}{3}\pi r^3

Question