Question

Find the volume of a sphere whose surface area is 154 cm²
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Answer 1

Given,

Surface area of sphere is 154 cm^2

Surface area of sphere = 4πr^2

$4 \times \frac{22}{7} \times {r}^{2} = 154 \\ {r}^{2} = \frac{154}{4} \times \frac{7}{22} \\ {r}^{2} = \frac{49}{4} \\ r = \sqrt{ \frac{49}{4} } \\ r = \frac{7}{2} \\ r = 3.5cm$

Volume of sphere = 4/3πr^3

$\frac{4}{3} \times \frac{22}{7} \times {3.5}^{3} \\ \frac{88}{21} \times 42.875 = 179.67 {cm}^{3}$

Therefore the volume of sphere is 179.67cm^3.

Answer 2

Given:-

The surface area of the sphere = 154cm²

To Find:-

The volume of the sphere.

Solution:-

Let the radius of the sphere be " r "

Surface area of the sphere = 4πr²

$\sf \implies 4 \pi r^2 = 154$

$\sf \implies 4\times \dfrac{22}{7}\times r^2 = 154$

$\sf \implies \dfrac{88}{7}\times r^2 = 154$

$\sf \implies r^2 = 154 \times \dfrac{7}{88}$

$\sf \implies r^2 = \dfrac{1078}{88}$

$\sf \implies r^2 = 12.25$

$\sf \implies r = \sqrt{12.25}$

$\sf \implies r = 3.5cm$

$\sf \therefore Radius \: of \: the \: sphere = 3.5cm$

$\sf Volume \: of \: the \: sphere = \dfrac{4}{3}\pi r^3$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{4}{3} \times \dfrac{22}{7} \times (3.5)^3$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{88}{21} \times 42.875$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 179.67cm^3$

$\underline{\boxed{\therefore \textsf{\textbf{Volume \: of \: the \: sphere = 179.67}}\bf cm^3}}$