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.