NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.2 – Part 3

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Q-9 Find

  1. The lateral or curved surface area of a closed cylindrical petrol storage tank that is in diameter and high.

  2. How much steel was actually used, if of the steel actually used was wasted in making the tank.

Solution:

Areas in a cylinder and its volume

Recap of Cylinder Areas and Volume

Areas in a cylinder and its volume

Solution (I)

The tank radius (r) The tank height (h)

Curved surface area =

Solution (II)

Total surface area of the tank

Now assume that is the actual steel used in making tank. Than we know that of actual steel used was wasted. Therefore the remaining must match the area of the tank.

Therefore,

Q-10 In the figure, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of and height of . A margin of 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.

the Frame of a Lampshade

The frame of a lampshade, frame diameter20cm, height30cm, margin2.5cm.

Solution: Note that he lampshade is a cylinder. Now,

  • The cloth cylinder radius (r)

  • Since, of margin must be added to both side of the height. Therefore, the cloth cylinder height (h)

  • Therefore, cloth required for covering the lampshade is the curved surface area of our cloth cylinder = =

Q-11 The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius and height The Vidyalaya was to supply the competitors with cardboard. If there were competitors, how much cardboard was required to be bought for the competition?

Solution:

  • Radius (r) of the penholder

  • Height (h) of the penholder

Cardboard required by 1 competitor, is found by realizing that the penholder has a base but no top. Therefore, area of cardboard required for 1 penholder = curved surface area + area of the base

Therefore, cardboard required for competitors

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