Question

The SA of a sphere is 5544sqcm.Find the volume.​

Answer 1

★Required Answer

Volume of the sphere = 38808cm^3

Given:-

• Surface Are of the sphere = 5544sqcm.

To Find:-

• Volume of the sphere

Concept:-

We are given that Surface area of the sphere is 5544sq.cm and we have to find the volume.Firstly we should find the radius of the sphere by equating the values in the equation of Surface Area of Sphere.Then,equate the values in the second equation to find the volume.

$\Large\boxed{\mathtt{Surface \: Area \: of \: a \: Sphere \: = \: 4\pi {r}^{2}}}$

By substituting given values in the equation let's find the radius.

$\implies\large\mathcal{4 \: \times \: \frac{22}{7} \: \times \: {r}^{2} \: = \: 5544}$

$\implies\large\mathcal{{r}^{2} \: = \: \frac{5544 \: \times \: 7}{4 \: \times \: 22}}$

$\implies\large\mathcal{{r}^{2} \: = \: \frac{38808}{88}}$

$\implies\large\mathcal{{r}^{2} \: = \: 441}$

$\implies\large\mathcal{r \: = \: \sqrt{441} }$

$\implies\large\mathcal{r \: = \:21cm}$

Hence,we got Radius of the Sphere as 21cm.

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$\Large\boxed{\mathtt{Volume \: of \: a \: Sphere \: = \: \frac{4}{3}\pi {r}^{3}}}$

By using this equation and substituting all values let's find the volume of the sphere

$\implies\large\mathcal{ \frac{4}{3} \: \times \: \frac{22}{7} \: \times \: 21 \: \times \: 21 \: \times \: 21}$

$\implies\large\mathcal{{4} \: \times \: 22 \:\times\: 21 \: \times \: 21}$

$\implies\large\mathcal{38808cm^{3} }$

Hence,we got the Volume of the Sphere as 38808cm^3

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More to Know:-

• A sphere is a solid figure that has no faces, edges, or vertices.

• It is completely round; it has no flat sides or corners.

• It is perfectly Symmitrical and it is jot a polyhedron.

• It has a surface.

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