# PracticeSurface Area

#### puremath

##### New member
If the surface area of a sphere is represented by 144pi, what is the volume in terms of pi?

Solution:

Let SA = surface area

SA = 4πr^2

Let V = volume

V = (4/3)π r^3

We are given the surface area to be 144 π.

Replace SA with 144π and solve for r, the radius.

144 π = 4πr^2

144π/4π = r^2

36 = r^2

Take the square root on both sides to find r = 6.

Now plug r = 6 in the volume formula above.

V = (4/3)π (6)^3

V = (4/3)π 216

216 ÷ 3 = 72

V = 4 π times 72

V = 288 π

Correct?

Last edited:

#### MarkFL

##### La Villa Strangiato
Math Helper
$$\displaystyle S=4\pi r^2\implies r=\frac{1}{2}\sqrt{\frac{S}{\pi}}$$

$$\displaystyle V=\frac{4}{3}\pi r^3=\frac{S}{3}r=\frac{S}{6}\sqrt{\frac{S}{\pi}}$$

Plugging in for $$S$$

$$\displaystyle V=24\pi\cdot12=288\pi\quad\checkmark$$

• puremath

#### puremath

##### New member
$$\displaystyle S=4\pi r^2\implies r=\frac{1}{2}\sqrt{\frac{S}{\pi}}$$

$$\displaystyle V=\frac{4}{3}\pi r^3=\frac{S}{3}r=\frac{S}{6}\sqrt{\frac{S}{\pi}}$$

Plugging in for $$S$$

$$\displaystyle V=24\pi\cdot12=288\pi\quad\checkmark$$
Finally did something worth boasting about.