Practice Surface 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

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.
 
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