# Ex.13.2 Q2 Surface Areas and Volumes - NCERT Maths Class 9

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## Question

It is required to make a closed cylindrical tank of height $$1 \,\rm{m}$$ and base diameter $$140 \,\rm{cm}$$ from a metal sheet. How many square metres of the sheet are required for the same?

Video Solution
Surface Areas And Volumes
Ex 13.2 | Question 2

## Text Solution

Reasoning:

The curved surface area of a right circular cylinder of base $$r$$  and height  $$h$$ is and its total surface area is \begin{align}2\pi r(r + h) \end{align}

What is the known?

Height and diameter of the cylindrical tank.

What is the unknown?

Square metres of the sheet required for making the cylindrical tank.

Steps:

Height of the tank $$(h)$$ = $$1 \,\rm{m}$$ = $$100 \,\rm{cm}$$

Diameter $$= 2r =$$ $$140 \,\rm{cm}$$

\begin{align}r = \frac{{140}}{2} = 70\,\,\rm{cm} \end{align}

Total surface area of the closed cylindrical tank

\begin{align} &= 2\pi r\,(r + h)\\&= 2 \times \frac{{22}}{7} \times 70(70 + 100)\\ &= 74800\,\,\rm{c{m^2}} \end{align}

Since,

\begin{align}100 cm &= \rm{1 m}\\\rm{100^2}c{m^2} &= \rm1\,\,{m^2}\\\rm74800\,\,c{m^2} &= \frac{{748000}}{{100 \times 100}}\\ & = \rm7.48\,\,{m^2} \end{align}

\begin{align}7.48\,{\rm{m^2}} \end{align} of the sheet is required for making the cylindrical tank.

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