Ex.13.8 Q7 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

Find the volume of a sphere whose surface area is \(\begin{align}154\,\,c{m^2} \end{align}\).

Text Solution

Reasoning:

Surface area of the sphere = \(4\pi r^2\)
Volume of the sphere=\(\begin{align}\frac{4}{3}\pi r^3\end{align}\)

What is known?

Surface area of the sphere.

What is unknown?

Volume of the sphere.

Steps:

Let the radius of the sphere be .

Surface area of the sphere

\[\begin{align}&={4 \pi r^{2}} \\ {\text { Surface area }}&={154 \mathrm{cm}^{2}} \\ r^{2} &=\frac{154}{4} \times \frac{7}{22} \\ r^{2} &=\frac{49}{4} \\ r &=\frac{7}{2} \mathrm{cm} \end{align}\]

Volume of the sphere

\[\begin{align}&={\frac{4}{3} \pi r^{3}} \\ &=\frac{4}{3} \times \frac{22}{7} \times\left(\frac{7}{2}\right)^{3} \\ &=\frac{539}{3} \mathrm{cm}^{3} \end{align}\]

Answer:

Volume of the sphere \(\begin{align} = 179\frac{2}{3}\,\,\,c{m^3} \end{align}\)