**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

= π*r*^{2} × *h *= π*r*^{2}*h *cubic units

**Volume of a cylinder = π r^{2}h**

*r *is the radius of the base and *h *is the
height of the right circular cylinder.

**Volume of Cylinder Formula**

**Volume of Cylinder Formula**

**Volume of a cylinder = π r^{2}h**

**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

*r*^{2}*h *= 22/7 × 7 × 7 × 10 = 1540 cm^{3}

**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 = π*r*^{2}*h
*

* *= 22/7 × 20 × 20 ×
14

=
22 × 800 = 17600 cm^{3}

**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 = π*r*^{2}*h
*= 22/7 × 3.5 × 3.5 × 5 = 192.5 m^{3}

1 m^{3} = 1000 litres

192.5 m^{3} = 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 2*k *and 3*k*,
respectively.

Again, let the heights of the first
and the second cylinder be 7*p *and 3*p*, respectively.

Volume of the first cylinder (V_{1})
= π*r*^{2}*h *= π(2*k*)^{2} × 7*p *= 28π*pk*^{2}

Volume of the second cylinder (V_{2})
= πr^{2}*h *= π(3*k*)^{2} × 3*p *= 27π*pk*^{2}

Therefore, V_{1}/ V_{2}
= 28π*pk*^{2}/27π*pk*^{2}

V_{1 }: V_{2} = 28 : 27

Hence, ratio of their volumes is 28 :
27.