Question

7. 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​

Answer 1

$Answer⬇️$

Here, h = 14 cm.

Radius of the pencil (R) = 7/ 2 mm = 0.35 cm.

Radius of the graphite (r) = 1/ 2 mm = 0.05 cm.

Volume of the the graphite = π r2h

= 22/ 7 × 0.05 × 0.05 × 14 cm³ = 0.11 cm³

Volume of the the wood = π (R2 – r2)h

= 22/ 7 × [(0.35)2 – (0.05)2] × 14 cm3

= 22/ 7 × 0.4 × 0.3 × 14 cm3 = 5.28 cm³

Hence, volume of the wood = 5.28 cm³ and volume of the graphite

= 0.11 cm³

Answer 2

Answer:

Here, h = 14 cm.

Radius of the pencil (R) = 7/ 2 mm = 0.35 cm.

Radius of the graphite (r) = 1/ 2 mm = 0.05 cm.

Volume of the the graphite = π r2h

= 22/ 7 × 0.05 × 0.05 × 14 cm³ = 0.11 cm³

Volume of the the wood = π (R2 – r2)h

= 22/ 7 × [(0.35)2 – (0.05)2] × 14 cm3

= 22/ 7 × 0.4 × 0.3 × 14 cm3 = 5.28 cm³

Hence, volume of the wood = 5.28 cm³ and volume of the graphite

= 0.11 cm³