NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.8 – Part 4

Volume of sphere=4/3 πr^3

Volume of Sphere

Volume of sphere=4/3 πr^3

Q-9 Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S' . Find the

  1. Radius r' of the new sphere,

  2. Ratio of SandS'.

Solution:

When the spheres are melted the volume of molten material remains the same.

  1. Volume of 27 solid sphere of radius r=27×43πr3

    Volume of the new sphere of radius r'=43πr'3 …………….equation (2)

    Since the volume must remain the same, therefore,

    • 43πr'3=27×43πr3

    • r'3=27r3

    • r'3=(3r)3

    • r'=3r

  2. Required ratio of surface area,

  • SS' = 4πr24πr'2

  • =r2(3r)2 (r'=3r)

  • =r29r2

  • =19 or the ratio is 1:9

Q-10 A capsule of medicine is in the shape of a sphere of diameter 3.5mm . How much medicine (in mm3 ) is needed to fill this capsule?

Solution:

Diameter of the spherical capsule =3.5mm

Therefore, radius (r) =3.522 (radius=diameter2)=1.76mm

Medicine needed for filling this capsule = Volume of this spherical capsule

  • =43πr3

  • =(43×227×1.76×1.76×1.76)mm3

  • =(8821×(1.76)3)

  • =22.84mm3(approx.)

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