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

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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?

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Surface Areas And Volumes
Ex 13.2 | Question 2

Text Solution



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.


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

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


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

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