EXAMPLES ON VOLUME OF CYLINDER

We can find the volume V of both a prism and a cylinder by multiplying the height by the area of the base. 

Let the area of the base of a cylinder be B and the height of the cylinder be h. Write a formula for the cylinder’s volume V.

V = Bh

The base of a cylinder is a circle, so for a cylinder,

B = πr²

Then, we have

V = πr²h cubic units

Example 1 :

Find the volume of a solid cylinder whose radius is 14 cm and height is 30 cm.

Solution :

We need to find the volume of the solid cylinder.

Radius of the cylinder  =  14 cm

Height of the cylinder  =  30 cm

Volume of the right circular cylinder  = πr²h

=  (22/7) · (14)² · 30

=  (22/7) · 14  · 14 · 30

=  18480 cubic.cm

Volume of the cylinder  =  18480 cubic.cm

Example 2 :

A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, then find the quantity of soup to be prepared daily in the hospital to serve 250 patients?

Solution :

Radius of the cylinder  =  7/2 cm

Height of the cylinder  =  4 cm

To find quantity of soup in one bowl,  we have to find the quantity of each bowl.

Volume of the right circular cylinder  =  πr²h

=  (22/7) · (7/2)²  · 4

=  (22/7) · (7/2) · (7/2) · 4

=  154 cm³

Volume of soup in one cylindrical bowl  =  154 cm³

Volume of soup in 250 cylindrical bowl  =  250 · 154

=  38500 cm³

1000 cm³  =  1 L

Therefore required quantity of soup  =  38500/1000

=  38.5 L

Required quantity of soup for 25 patients = 38.5 L

Example 3 :

The sum of the base radius and the height of a solid cylinder is 37 cm. If the total surface area of the cylinder is 1628 sq.cm, then find the volume of the cylinder.

Solution :

Let r and h are the radius and height of the cylinder respectively

Sum of radius and height  =  37

r + h  =  37 cm

Total surface area of cylinder  =  1628 sq.cm

2πr(h + r)  =  1628

2πr(37)  =  1628

2πr  =  1628/37

2 · (22/7) · r = 44

r  =  44 · (1/2) · (7/22)

r  =  7

7 + h  =  37

h  =  30 cm

Volume of the right circular cylinder =  πr²h

=  (22/7) ·7²·30

=  (22) x (7) x (30)

=  4620 cm³

Volume of cylinder  =  4620 cm³

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