Question

It the total surface area of sphere is 154 cm find its tatal volumi​

Answer 1

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Q - If the Total Surface Area of a sphere is 154 cm² , Find it's volume .

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Given :

• T.S.A. = 154 cm²

To Find :

• Volume = ?

Solution :

Let the radius of the sphere be r

$\rm \: tsa = 154 \: {cm}^{2}$

$\rm \: 4 \pi {r}^{2} = 154 \: {cm}^{2}$

$\mapsto \rm\: 4 \times \dfrac{ \cancel{22}}{7} \times {r}^{2} = \cancel{154} \: {cm}^{2}$

$\mapsto \rm \: \frac{4}{7} {r}^{2} = 7$

$\mapsto \rm \: {r}^{2} = \frac{7 \times 7}{4}$

$\mapsto \rm \: r = \sqrt{ \frac{7 \times 7}{4} }$

$\mapsto \boxed{ \rm \: r = \frac{7}{2} cm}$

Now ,

Using the Formula to Find Volume ..

$\rm \longrightarrow \: volume_{sphere} = \frac{4}{3} \pi {r}^{3}$

$\implies \rm \: v = \frac{4}{3} \times \frac{22}{7} \times {( \frac{7}{2} )}^{3}$

$\implies \rm \: v = \frac{ \cancel4}{3} \times \frac{ \cancel{22}}{ \cancel7} \times \frac{ \cancel7 \times 7 \times 7}{ \cancel2 \times \cancel2 \times \cancel2}$

$\implies \rm \: v = \frac{11 \times 7 \times 7}{3}$

$\implies \boxed{\rm \: volume \: = \frac{539}{3} {cm}^{3}}$

or

$\implies \boxed{ \rm \: volume = 179.66 \: {cm}^{3} }$

So , It is the total volume..