Question

Find the surface area (in terms of π) of a sphere if its volume is 972 π.

Answer 1

Surface area of sphere is $Surface\,\,Area=324\pi$

Step-by-step explanation:

We need to find the surface area of the sphere while we are given volume of sphere = 972π

The formula used to find surface area is:

$Surface\,\,Area=4\pi r^2$

We need to find radius of sphere

We are given Volume = 972π, using this volume we can find radius of sphere

The formula used to find volume is:

$Volume=\frac{4}{3}\pi r^3$

Putting values and finding r

$972\pi =\frac{4}{3}\pi r^3$

$r^3=\frac{972\pi *3}{4\pi } \\r^3=729$

Taking cube root on both sides

$\sqrt[3]{r^3}=\sqrt[3]{729}\\ r=9$

So, Radius of sphere r=9

Now finding surface area:

$Surface\,\,Area=4\pi r^2$

$Surface\,\,Area=4\pi (9)^2$

$Surface\,\,Area=4\pi 81$

$Surface\,\,Area=324\pi$

So, surface area of sphere is $Surface\,\,Area=324\pi$

Keywords: Surface area of sphere

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