#### puremath

##### Active 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?

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?

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