Question

The surface area of a sphere is 616 cm. find its volume

Answer 1

$\huge\underline\mathcal\color{olive}Given$

• The surface area of a sphere is 616cm.

$\huge\underline\mathcal\color{olive}ToFind$

• Volume of the sphere.

$\rule{300}{2}$

$\huge\underline\mathcal\color{olive}Solution$

We know that,

Area of a sphere=$4\pi \: {r}^{2}$

By condition,

$\sf{\implies 616= 4 \times \frac{22}{7} \times {r}^{2} }$

$\sf{\implies 616 = \frac{88}{7} \times {r}^{2} }$

$\sf{\implies 88 {r}^{2} = 616 \times 7}$

$\sf{\implies 88 {r}^{2} = 4312}$

$\sf{\implies {r}^{2} = \cancel\frac{4312}{88} }$

$\sf{\implies r = 7}$

Therefore the radius of the sphere is 7.

Now,

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

$\sf{Volume \: of \: the \: sphere = \frac{4}{3} \times \frac{22}{7} \times 7 \times 7 \times 7 }$

$\sf{Volume \: of \: the \: sphere = \frac{4}{3} \times 22 \times 7 \times 7}$

$\sf{Volume \: of \: the \: sphere = \frac{4312}{3} }$

$\sf{Volume \: of \: the \: sphere = 1437.33c {m}^{3} }$

$\rule{300}{2}$

$\sf{Hence~the~volume~of~the~sphere~is~=1437.33{cm}^{3}}$

$\huge\underline\mathcal\color{olive} ThankYou$

Answer 2

${ \huge{ \bold{\underline{ \underline{ \red{Solution:-}}}}}}$

Given:-

ꔷ Surface area of the sphere = 616cm.

To Find:-

ꔷ Volume

NoW,

Area of the sphere = 4πr^2

A/Q,

➡ 616 = 4πr^2

➡ 616 = 4× 22/7× × r^2

➡616 = 88/7 ×r^2

➡88r^2 = 616× 7

➡ 88r^2 = 4312

➡ r^2 = 4312/88

➡ r = 7 cm.

Therefore, the radius of the sphere = 7 cm

NoW,

Volume of the sphere = 4/3πr^2

➡ Volume the sphere = 4/3 ×22/7×7×7×7

➡ Volume the sphere = 4312/7

➡Volume the sphere = 1437.33cm^3

Hence,the volume of the sphere = 1437.33cm^3