NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.4 – Part 3

Surface area of sphere=4πr^2

Surface Area of Sphere

Surface area of sphere=4πr^2

Q-7 The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.


  • Consider the diameter of earth be r and that of the moon will be r4

  • Radius of the earth =r2

  • Radius of the moon =r8

Ratio of their surface area

  • 4π(r8)24π(r2)2

  • (16414)

  • 464

  • 116

So, 1:16 the ratio of their surface areas.

Q-8 A hemispherical bowl is made of steel, 0.25cm thick. The inner radius of the bowl is 5cm . Find the outer curved surface area of the bowl.


  • Inner radius of the bowl (r) =5cm

  • Thickness of the steel =0.25cm

    Outer radius (R)

  • (r+0.25)cm

  • (5+0.25)cm

  • 5.25cm

Outer curved surface

  • 2πR2

  • (2×227×5.25×5.25)cm2 ( π=227 )

  • 173.25cm2

Q-9 A right circular cylinder just encloses a sphere of radius r (see Fig). Find

  1. Surface area of the sphere,

  2. Curved surface area of the cylinder,

  3. Ratio of the areas obtained in (i) and (ii).

Ellipse c Ellipse c: Ellipse with foci A, C passing through E Ellipse c_1 Ellipse c_1: Ellipse with foci A_1, C_1 passing through E_1 Circle d Circle d: Circle through G with center F Segment f Segment f: Segment [A, B] Segment g Segment g: Segment [A, C] Segment h Segment h: Segment [C, D]

a Right Circular Cylinder

A right circular cylinder, sphere of radius r


  1. The surface area of the sphere with radius r=4πr2

  2. The right circular cylinder just encloses a sphere of radius r.

    The radius of the cylinder =r and its height =2r .

    Curved surface of cylinder

    • 2πrh

    • 2π×r×2r

    • 4πr2

  3. Ratio of the areas

  • 4πr2:4πr2

  • 4πr24πr2

  • 11

Ratio of area 1:1

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