3 Tutor System
Starting just at 265/hour

# 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, and the volume of the wood and that of the graphite.

Given :
Radius (R) of pencil = $$\frac{7}{2} mm = 3.5 mm = 0.35 cm$$
Radius (r) of graphite = $$\frac{1}{2} mm = 0.5 mm = 0.05 cm$$
Height (h) of pencil = 14 cm

We know that,

Volume of wood in pencil
= $${\pi} ({R}^2 - {r}^2) h$$
= $$\frac{22}{7} × ({0.35}^2 - {0.05}^2) × 14$$ $${cm}^3$$
= $$\frac{22}{7} × (0.1225 - 0.0025) × 14$$ $${cm}^3$$
= 44 × 0.12 $${cm}^3$$
= 5.28 $${cm}^3$$

Similarly, Volume of graphite in pencil
= $${\pi} {r}^2 h$$
= $$\frac{22}{7} × {0.05}^2 × 14$$ $${cm}^3$$
= 44 × 0.0025 $${cm}^3$$
= 0.11 $${cm}^3$$