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