A solid sphere has a volume of 36\pi cubic centimeters. What is the radius, in centimeters… — SAT

A solid sphere has a volume of $36\pi$ cubic centimeters. What is the radius, in centimeters, of the sphere?

Answer: 3 cm

The radius of the sphere is 3 centimeters.

The volume of a sphere is given by the formula

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

. Substituting

36\pi

for

V

gives

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

. Dividing both sides by

\pi

results in

36 = \frac{4}{3}r^3

. Multiplying both sides by

\frac{3}{4}

yields

27 = r^3

. Taking the cube root of both sides gives

r = 3

. Thus, the radius of the sphere is 3 centimeters.

State the sphere volume formula.

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

The volume of a sphere is calculated using this standard formula relating volume to radius.

Substitute the given volume value into the formula.

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

The problem specifies the volume is

36\pi

cubic centimeters.

Solve for the radius cubed (

r^3

r^3 = 27

Dividing both sides of the equation by

\pi

yields

36 = \frac{4}{3}r^3

, and multiplying both sides by

\frac{3}{4}

isolates

r^3

to give 27.

Take the cube root of both sides to find the radius (

r

r = 3

The cube root of 27 is 3, since

3 \times 3 \times 3 = 27

Using the volume of a sphere formula to solve for an unknown radius.

Question