NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.8 – Part 2

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Volume formula,sphere volume=4/3 πr^3, hemisphere=2/3 πr^3

Volume Formula

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Q-4 The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

Solution:

If the diameter is one-forth then radius of moon would also be one-fourth of the radius of the earth.

Let radius of the moon be , then radius of the earth

Volume of the moon

Volume of the earth

Or that is, the volume of the moon is of the volume of the earth.

Q-5 How many liters of milk can a hemispherical bowl of diameter hold?

Solution:

Given,

  • Diameter of a hemispherical bowl

  • Radius(r)

Volume of the hemispherical bowl is

  • (Since 1 liter = 1000 cubic centimeters)

Q-6 A hemispherical tank is made up of an iron sheet thick. If the inner radius is, then find the volume of the iron used to make the tank.

Solution:

Given a hemispherical tank with some thinkness,

  • Internal radius

  • External radius

Volume of iron used = External volume – Internal volume