NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.6 – Part 3
Q6 The capacity of a closed cylindrical vessel of height is liters. How many square meters of metal sheet would be needed to make it?
Solution:

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.
Q7 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.
Solution:

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
Q8 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?
Solution:

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)