Ex.13.2 Q10 Surface Areas and Volumes - NCERT Maths Class 9

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Question

In the below figure, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of \(20 \,\rm{}cm\) and height of \(30 \,\rm{}cm.\) A margin of \(2.5 \,\rm{}cm.\) is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.

 Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-2 | Question 10

Text Solution

 

Reasoning:

The curved surface area of a right circular cylinder of base radius r and height h is and its total surface area \(\begin{align}2\pi r(r + h) \end{align}\).The amount of cloth required to cover the cylinder will be equal to surface are of cylinder. (Here height will will equal to the height of cylinder plus \(2.5 \,\rm{}cm.\) margin on both sides).

What is the known?

The height and diameter of the frame of lampshade. And the margin of \(2.5 \,\rm{}cm.\) for folding.

What is the unknown?

Cloth required for covering the lamp shade.

Steps:

Diameter \(= 2r = 20\,\rm{}cm\)

              \(r = 10 \rm{}\,cm\)

Height of the lamp shade \(= 30\,\rm{} cm + 2.5 \,\rm{}cm\) for both side folding

Total height of the cloth \(= 35 \,\rm{}cm\)

Cloth required is the curved surface area

\[\begin{align}&=2\pi rh\\ &= 2 \times \frac{{22}}{7} \times 10 \times 35\\ &= 2200\,\,\rm{c{m^2}} \end{align}\]

Cloth required \(\begin{align} = 2200\,\,\rm{{cm^2}} \end{align}\)