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'.


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?


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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