Question

How much air does spherical balloon with radius 4.2 contain? how much will it contain if the radius is halved?

Answer 1

$\huge\mathbb{SOLUTION:-}$

We have to find the volume of sphere

$\bf\underline{\underline{According\:to\: Question:-}}$

• Volume of sphere if radius =(4.2)

$\begin{cases}\sf{radius=4.2}\end{cases}$

$\boxed{\sf{Volume\:of\:sphere=\frac{4}{3}\pi r{}^{3}}}$

$\sf volume=\frac{4}{3}\times \frac{22}{\cancel7}\times 4.2\times 4.2\times \cancel{4.2}\\ \\ \sf\implies Volume=\frac{4\times 22\times 4.2\times 4.2\times 0.6}{3}\\ \\ \sf\implies Volume=\frac{931.392}{3}=310.464cu.unit\\ \\ \sf\implies Volume\:of\: spherical\:ball_{r=4.2}=310.464cu.unit$

$\large{\boxed{\bf{Volume\:if\:radius \:is\:halved}}}$

• Volume of sphere if radius

$\begin{cases}\sf{radius=\frac{4.2}{2}=2.1}\end{cases}$

$\sf volume=\frac{4}{3}\times \frac{22}{\cancel7}\times 2.1\times 2.1\times \cancel{2.1}\\ \\ \sf\implies Volume=\frac{4\times 22\times 2.1\times 2.1\times 0.3}{3}\\ \\ \sf\implies Volume=\frac{116.424.72}{3}=38.808cu.unit\\ \\ \sf\implies Volume\:of\: spherical\:ball_{r=2.1}=38.808cu.unit$

$\boxed{\sf{\purple{Volume\:if_{r=4.2}=310.464cu.unit}}}$

$\boxed{\sf{\green{Volume\:if_{r=2.1}=38.808cu.unit}}}$

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Answer 2

$\underline \mathbb{SOLUTION}$

》TO FIND THE VOLUME OF SPHERE.

VOLUME OF SPHERE IF RADIUS = 4.2

$= > volume \: of \: sphere = \frac{4}{3} \pi {r}^{3}$

$volume = \frac{4}{3} \times \frac{22}{7} \times 4.2 \times 4.2 \times 4.2$

$= > volume = \frac{4 \times 22 \times 4.2 \times 4.2 \times 4.2}{3}$

$= > volume = \frac{931.392}{3}$

$= > 310.464 \: unit$

WHEN VOLUME OF RADIUS IS HALVED...

WHEN RADIUS = 2.1 , VOLUME OF SPHERE = ?

$= > volume = \frac{4}{3} \times \frac{22}{7} \times 2.1 \times 2.1 \times 2.1$

$= > volume = \frac{4 \times 22 \times 2.1 \times 2.1 \times 0.3}{3}$

$= > volume = \frac{116.424}{3}$

$= > 38.808 \: cu \: unit$

$= > volume \: of \: spherical \: ball \: with \: radius \: 2.1 = 38.808$

•VOLUME IF R= 4.2

》310.464 UNIT

•VOLUME IF R= 2.1

》38.808 UNIT

_______________________________________

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