Question

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Surface area of a Sphere is $\bf 5544 cm^2$
Find its volume

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Answer 1

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Answer 2

Answer:

Given :-

• Surface area of a sphere is 5544 cm².

To Find :-

• What is the volume.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{Surface\: Area\: Of\: Sphere =\: 4{\pi}{r}^{2}}}}$

$\longmapsto \sf\boxed{\bold{\pink{Volume\: Of\: Sphere =\: \dfrac{4}{3}{\pi}{r}^{3}}}}$

where,

• r = Radius

Solution :-

First, we have to find the radius of the sphere :

So, let the radius of the sphere be r cm

Given :

• Surface area = 5544 cm²

According to the question by using the formula we get :

$\implies \sf 4 \times \dfrac{22}{7} \times {r}^{2} =\: 5544$

$\implies \sf {r}^{2} =\: \dfrac{5544 \times 7}{4 \times 22}$

$\implies \sf {r}^{2} =\: \dfrac{\cancel{38808}}{\cancel{88}}$

$\implies \sf {r}^{2} =\: 441$

$\implies \sf r =\: \sqrt{441}$

$\implies \sf\bold{\purple{r =\: 21\: cm}}$

Hence, the radius of the sphere is 21 cm.

Now, we have to find the volume of its sphere :

Given :

• Radius = 21 cm

According to the question by using the formula we get :

$\implies \sf Volume\: Of\: Sphere =\: \dfrac{4}{3} \times \dfrac{22}{7} \times {(21)}^{3}$

$\implies \sf Volume\: Of\: Sphere =\: \dfrac{4}{3} \times \dfrac{22}{\cancel{7}} \times {\cancel{9261}}$

$\implies \sf Volume\: Of\: Sphere =\: \dfrac{4}{3} \times 22 \times 1323$

$\implies \sf Volume\: Of\: Sphere =\: \dfrac{4}{\cancel{3}} \times {\cancel{29106}}$

$\implies \sf Volume\: Of\: Sphere =\: 4 \times 9702$

$\implies \sf\bold{\red{Volume\: Of\: Sphere =\: 38808\: {cm}^{3}}}$

$\therefore$ The volume of the sphere is 38808 cm³.