Ex.13.8 Q6 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

A hemispherical tank is made up of an iron sheet \(1\rm{cm} \)thick. If the inner radius is \(1\rm{m}\), then find the volume of the iron used to make the tank.

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Surface-Areas-And-Volumes
Ex exercise-13-8 | Question 6

Text Solution

Reasoning:

Volume of the hemisphere \(\begin{align} = \frac{2}{3} \end{align}\) \(\pi r^{3}\) \(3\) where r will be equal to the summation of thickness of sheet and inner radius of tank.

What is known?

Inner radius and thickness of the iron sheet.

What is unknown?

Volume of the iron used.

Steps:

Inner radius\( (π‘Ÿ) = 1 \,\rm{π‘š}\)
Thickness of the sheet \(= 1 \,\rm{π‘π‘š} = .01 \,\rm{π‘š}\)

Outer radius (R) \(=\) inner radius\(+\)thickness 

\[\begin{align}={1 \mathrm{m}+0.01 \mathrm{m}=1.01 \mathrm{m}}\end{align}\]

Volume of the iron used to make the tank 

\[\begin{align}&=\frac{2}{3} \pi\left(R^{3}-r^{3}\right)\\&={\frac{2}{3} \times \frac{22}{7} \times\left[1.01^{3}-1^{3}\right]} \\ &={.06348 \mathrm{m}^{3}}\end{align}\]

Answer:

Volume of the iron used\(\begin{align} = .06348\,\,{m^3} \end{align}\).

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