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 Equation and surface area Equation are melted to form a sphere with surface area Equation . Find the

  1. Radius Equation of the new sphere,

  2. Ratio of Equation

Solution:

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

  1. Volume of Equation solid sphere of radius Equation

    Volume of the new sphere of radius Equation …………….equation (2)

    Since the volume must remain the same, therefore,

    • Equation

    • Equation

    • Equation

    • Equation

  2. Required ratio of surface area,

  • Equation = Equation

  • Equation Equation

  • Equation

  • Equation or the ratio is Equation

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

Solution:

Diameter of the spherical capsule Equation

Therefore, radius (r) Equation Equation

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

  • Equation

  • Equation

  • Equation

  • Equation

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