NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.2 – Part 1

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Q-1 The curved surface area of a right circular cylinder of height 14cm is 88cm2 . Find the diameter of the base of the cylinder.

A rectangle rolled into a cylinder

Curved Surface of a Cylinder Made From a Rectangle

A rectangle rolled into a cylinder

Understanding curved surface area of a cylinder.

Curved Surface Area of a Cylinder as the Area of a Rectangle

Understanding curved surface area of a cylinder.

Solution:

The radius of the base is r and the height h=14cm of the cylinder. Therefore, curved surface area of cylinder

  • 2πr×h=88cm2 (Given)

  • 2×227×r×14=88 (π=227)

  • r=882×227×14

  • r=88×72×22×14

  • r=1cm

So, the diameter of the base is = 2r=2×1=2cm

Q-2 It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same?Solution:

Total surface area of a cylinder

Total Surface Area of Cylinder

Total surface area of a cylinder

We are given that diameter of base =140cm=>r=1402=70cm=0.7m and Height (h)=1m

Therefore, metal sheet required to make a closed cylindrical tank = 2πr(h+r)

  • (2×227×0.7)(1+0.7)m2 (π=227)

  • (2×22×0.1×1.7)m2

  • 7.48m2

Q-3 A metal pipe is 77cm long. The inner diameter of a cross section is 4cm , the outer diameter being 4.4cm (see Fig.). Find its

  1. Inner curved surface area,

  2. Outer curved surface area,

  3. Total surface area.

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 Segment f Segment f: Segment [D, E] Segment g Segment g: Segment [F, G]

a Metal Pipe

A metal pipe is 77cm long, Inner diameter is4cm, outer diameter is 4.4cm

Solution:

External radius is R and the internal radius is r the length of the pipe is h , therefore

  • R=4.42cm=2.2cm

  • r=42cm=2cm

  • h=77cm

  1. Inner curved surface

    • 2πrhcm2

    • 2×227×2×77cm2 (π=227)

    • 968cm2

  2. Outer curved surface

    • 2πRhcm2

    • 2×227×2.2×77cm2 ( π=227 )

    • 1064.8cm2

  3. Total surface area of a pipe = Inner curved surface area + outer curved surface area + areas of two base

  • 2πrh+2πRh+2π(R2r2)

  • [968+1064.8+(2×227)(4.844)]cm2 ( π=227 )

  • (2032.8+447×0.84)cm2

  • (2032.8+5.28)cm2=2038.08cm2

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