NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.6 – Part 3

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Formulas for volume of common solids

Volumes of Common Solids

Formulas for volume of common solids

Q-6 The capacity of a closed cylindrical vessel of height is liters. How many square meters of metal sheet would be needed to make it?


  • Consider the radius of the cylinder to be

  • Height(h) of cylindrical vessel is

  • Since 1 cubic meter = 1000 liter. Therefore, volume of cylindrical vessel

So, the radius of the base of vessel

Total surface area of the cylindrical vessel

So, of the metal sheet would be required to make the cylindrical vessel.

Q-7 A lead pencil consist of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is and the diameter of the graphite is . If the length of the pencil is , find the volume of the wood and that of the graphite.


Cylinder of Wood

Cylinder of wood with solid cylinder of graphite filled in the interior.

  • Diameter of the graphite cylinder

  • Radius

  • Length of graphite

Volume of the graphite cylinder

Diameter of the pencil

  • Therefore, radius

  • Length of pencil

Volume of the pencil

Now pencil has wood and graphite, therefore volume of wood = volume of the pencil - volume of the graphite

Q-8 A patient in a hospital is given soup daily in a cylindrical bowl of diameter . If the bowl is filled with soup to a height of , how much soup the hospital has to prepare daily to serve patients?


  • Diameter of the cylindrical bowl

  • Therefore, radius

  • Height of serving bowl

So, soup saved in one serving = volume of the bowl

Volume of soup given to patients

  • Liters ( 1 liter = 1000 cubic centimeter)

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