Question

How much air is to be pumped to a sphere of radius 14cm to become its
total surface area 9856cm??​

Answer 1

The amount to air to be pumped is 80490.66 cm³

Step-by-step explanation:

Given:

Radius of a sphere is 14 cm

To find out:

The air to be pumped in sphere so that its surface area becomes 9856 cm²

Solution:

We know that surface area of a sphere of radius r is given by

$S=4\pi r^2$

Given

$S=9856$ cm²

Thus,

$4\pi r^2=9856$

$\implies 4\times \frac{22}{7} r^2=9856$

$\implies r^2=\frac{7}{22\times 4}\times 9856$

$\implies r^2=784$

$\implies r=\sqrt{784}$

$\implies r=28$ cm

Thus, the volume of the air in the sphere of 28 cm radius

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

$\implies V=\frac{4}{3}\times\frac{22}{7}\times 28^3$

$\implies V=91989.33$ cm³

Volume of the air in the sphere of 14 cm radius

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

$\implies V'=\frac{4}{3}\times\frac{22}{7}\times 14^3$

$\implies V'=11498.67$ cm³

Volume of air to be pumped

$=V-V'$

$=80490.66$ cm³

Hope this answer is helpful.

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