# A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

**Solution:**

Since the lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior, the height of the graphite and wood will be the same as the height of the pencil.

Volume of the wood can be calculated by subtracting volume of graphite from volume of the pencil.

Volume of a cylinder of base radius, r and height, h = πr^{2}h

For graphite:

Diameter of the graphite = 1 mm

Radius (r) = 1 mm = 0.5/10 cm = 0.05 cm

h = 14 cm

Volume of the graphite = πr^{2 }h

= 22/7 × 0.05 cm × 0.05 cm × 14 cm

= 0.11 cm³

For pencil:

Diameter of the pencil = 7 mm

Radius (R) = 7 / 2 mm = 3.5/10 cm = 0.35 cm

h = 14 cm

Volume of the pencil = π R^{2} h

= 22/7 × 0.35 cm × 0.35 cm × 14 cm

= 5.39 cm^{3}

Volume of wood = Volume of the pencil – Volume of the graphite

= 5.39 cm^{3} - 0.11cm^{3}

= 5.28 cm^{3}

The volume of the wood is 5.28 cm^{3} and the volume of graphite is 0.11 cm^{3}.

**Video Solution:**

## A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

### NCERT Solutions for Class 9 Maths - Chapter 13 Exercise 13.6 Question 7:

**Summary:**

It is given that the lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, we have found that the volume of the wood is 5.28 cm^{3} and the volume of graphite is 0.11 cm^{3}.