NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.8 – Part 1

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Volume of sphere=4/3 πr^3

Volume of Sphere

Volume of sphere=4/3 πr^3

Q-1 Find the volume of a sphere whose radius is

  1. 7cm

  2. 0.63m

Solution:

  1. Radius of the sphere (r)=7cm

    So, Volume of the sphere

    • = 43πr3

    • = (43×227×7×7×7)cm3

    • = 43123cm3

    • = 1437.33cm2

  2. Radius of the sphere (r)=0.63m

    Volume of the sphere

  • = 43πr3

  • = (43×227×0.63×0.63×0.63)m3

  • = 1.05m3

Q-2 Find the amount of water displaced by a solid spherical ball of diameter.

  1. 28cm

  2. 0.21m

Solution:

  1. Spherical ball’s diameter is =28cm

    Radius =282cm=14cm

    Amount of water displaced by the spherical ball = Volume of the ball

    • = 43πr3

    • = (43×227×14×14×14)cm3

    • = 344963cm3

    • = 1498.66cm3

  2. The spherical ball’s diameter =0.21m

    Radius (r)=0.212m=0.105m

    Amount of water displaced by the spherical ball = Volume of the ball

  • = 43πr3

  • = (43×227×0.105×0.105×0.105)m3

  • = 0.004851m3

Q-3 The diameter of a metallic ball is 4.2cm . What is the mass of the ball, if the density of the metal is 8.9gpercm3 ?

Solution:

  • Diameter of the ball =4.2cm

  • Radius =(4.22)cm=2.1cm (radius=diameter2)

Volume of the ball

  • = 43πr3

  • = (43×227×2.1×2.1×2.1)cm3

  • = 38.808cm3

Density of the metal is 8.9gpercm3

Therefore, mass of the ball =(38.808×8.9)g=345.3912g

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