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Volume and Surface Area of a Cylinder


Cylinder

  • Solids like measuring jar,
  • circular pillars,
  • circular pencils,
  • road rollers
  • and gas cylinder, etc…

These shapes are called cylindrical shape.

Volume of a Cylinder

For a cylinder of base radius = r and height of the cylinder = h

Volume of a Cylinder

Then we have

V = (πr2 h) cubic units

where,
V = Volume of Cylinder
π (pi)= 3.14159265358979 but we generally take 3.14 (constant)
r = Radius of circular surface of Cylinder (as shown in above figure)
h = Height of Cylinder (as shown in above figure)

Surface Area of a Cylinder

Surface Area of a Cylinder

 

 

 

 

 

 

 

 

The area of the top = πr2
The are of the bottom = πr2

Area of the Side

 

 

 

 

 

 

 

Area of the Side = 2πrh

Therefore total Surface area can be given by,
Surface Area of a Cylinder = 2πrh +2πr2

Surface Area of a Cylinder = 2πr(r+h)

Examples

Question 1: Calculate the volume of a given cylinder having height 30 cm and base radius of 14 cm. (Take pi = 22/7)

Solution:

Given:

Height = 30 cm

radius = 14 cm

we know that;

Volume, V = πr2h cubic units

V=(22/7) × 14 × 14 × 30

V= 18480 cm3

Therefore, the volume of a cylinder = 18480 cm3

Question 2: Calculate the radius of the base of a cylindrical container of volume 450 cm3. Height of the cylindrical container is 40 cm. (Take pi = 22/7)

Solution:

Given:

Volume = 450 cm3

Height = 35 cm

We know from the formula of cylinder;

Volume, V = πr2h cubic units

So, 450 = (22/7) × r2 × 35

r2 = (450 × 7)/(22 × 35) = 3150/770 = 4

Therefore, r = 2 cm

Therefore, the radius of a cylinder = 2 cm.

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