Volume of Cylinder
We have observed that a cuboid is made up with the rectangles. A
right circular cylinder is also made up with circles (circular discs) of the
same size stacked together one above the other.
We know that the volume of a cuboid = l × b × h = (l × b) × h = Area of base × height
= πr2 × h = πr2h cubic units
Volume of Cylinder Formula
Volume of a cylinder = πr2h
Example 1: A circular cylinder has base
radius 7 cm and height 10 cm. Find the volume of the
cylinder.
Solution: Here, r = 7 cm
and h = 10 cm
Example 2: The diameter of a cylinder is 40
cm and the height of the cylinder is 14 cm. Find the volume of the cylinder.
Solution:
Given, diameter = 40 cm
Radius (r) = Diameter/2 = 40/2 = 20 cm
Height (h) = 14 cm
∴Volume
of the cylinder = πr2h
= 22/7 × 20 × 20 ×
14
=
22 × 800 = 17600 cm3
Example 3: A cylindrical water tank has the
diameter of 7 m and height 5 m. How many litres of water can be stored in the
tank?
Solution:
Given, the diameter of the cylindrical water tank = 7 cm
Radius of the water tank = 7/2 = 3.5 m
Height of the water tank = 5 m
Volume of water in the tank = πr2h
= 22/7 × 3.5 × 3.5 × 5 = 192.5 m3
1 m3 = 1000 litres
192.5 m3 = 192.5 × 1000 =
192500 litres
Hence, 192500 litres of water can be
stored in the tank.
Example 4: The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 7 :
3. Find the ratio of their volumes.
Solution: Let
the radii of the first and the second cylinder be 2k and 3k,
respectively.
Again, let the heights of the first
and the second cylinder be 7p and 3p, respectively.
Volume of the first cylinder (V1)
= πr2h = π(2k)2 × 7p = 28πpk2
Volume of the second cylinder (V2)
= πr2h = π(3k)2 × 3p = 27πpk2
Therefore, V1/ V2
= 28πpk2/27πpk2
V1 : V2 = 28 : 27
Hence, ratio of their volumes is 28 :
27.