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

Q-9 Find

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

  2. How much steel was actually used, if Equation 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) Equation The tank height (h) Equation

Curved surface area = Equation

  • Equation

  • Equation

Solution (II)

Total surface area of the tank

  • Equation

  • Equation

  • Equation

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

Therefore, Equation

  • Equation

  • Equation

  • Equation

  • Equation

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 Equation and height of Equation . A margin of Equation 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.

Ellipse c Ellipse c: Ellipse with foci A, B passing through C Ellipse c Ellipse c: Ellipse with foci A, B passing through C Ellipse c_1 Ellipse c_1: Ellipse with foci A_1, B_1 passing through C_1 Ellipse c_1 Ellipse c_1: Ellipse with foci A_1, B_1 passing through C_1 Ellipse c_1 Ellipse c_1: Ellipse with foci A_1, B_1 passing through C_1 Segment f Segment f: Segment [D, E] Segment f Segment f: Segment [D, E] Segment g Segment g: Segment [F, G] Segment g Segment g: Segment [F, G] Segment h Segment h: Segment [H, I] Segment h Segment h: Segment [H, I] Segment i Segment i: Segment [J, K] Segment i Segment i: Segment [J, K] Point D Point D: Point on c Point D Point D: Point on c Point D Point D: Point on c Point E Point E: Point on c_1 Point E Point E: Point on c_1 Point E Point E: Point on c_1 Point F Point F: Point on c Point F Point F: Point on c Point F Point F: Point on c Point G Point G: Point on c_1 Point G Point G: Point on c_1 Point G Point G: Point on c_1 Point H Point H: Point on f Point H Point H: Point on f Point H Point H: Point on f Point I Point I: Point on g Point I Point I: Point on g Point I Point I: Point on g Point J Point J: Point on f Point J Point J: Point on f Point J Point J: Point on f Point K Point K: Point on g Point K Point K: Point on g Point K Point K: Point on g

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) Equation

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

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

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 Equation and height Equation The Vidyalaya was to supply the competitors with cardboard. If there were Equation competitors, how much cardboard was required to be bought for the competition?

Solution:

  • Radius (r) of the penholder Equation

  • Height (h) of the penholder Equation

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

  • Equation

  • Equation

  • Equation

  • Equation

  • Equation

Therefore, cardboard required for Equation competitors Equation

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