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

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

Volume Formula

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

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?


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 r , then radius of the earth =4r

Volume of the moon =V1=43π(r)3

Volume of the earth =V2=43π(4r)3=43πr3×64=V164

Or V1=164V2 that is, the volume of the moon is 164 of the volume of the earth.

Q-5 How many liters of milk can a hemispherical bowl of diameter 10.5cm hold?



  • Diameter of a hemispherical bowl =10.5cm

  • Radius(r) =(10.52)cm=5.25cm

Volume of the hemispherical bowl is 23πr3

  • =(23×227×5.25×5.25×5.25)cm3

  • =303.1875cm3

  • =(303.18751000)liters (Since 1 liter = 1000 cubic centimeters)

  • =0.3031875liters(approx.)

Q-6 A hemispherical tank is made up of an iron sheet 1cm thick. If the inner radius is 1m , then find the volume of the iron used to make the tank.


Given a hemispherical tank with some thinkness,

  • Internal radius =r=1m

  • External radius =R=(1+0.1)cm=1.01cm

Volume of iron used = External volume – Internal volume

  • =23πR323πr3

  • =23π(R3r3)

  • =23×227×[(1.01)3(1)3]m3

  • =4421×(1.0303011)m3

  • =(4421×0.030301)m3

  • =0.06348m3(approx.)

Explore Solutions for Mathematics

Sign In