Question

A pencil of diameter 10.5 mm and length 14.4 cm has a lead of diameter 1.75 mm. Find the volume of the wood and of the lead used in making 100 pencils

Answer 1

Volume of pencil =12127.5mm^2
Volume of lead=346.5mm^2
Total volume =12474mm^2

Answer 2

Volume of the wood and of the lead used in making 100 pencils is 1212.75 cm³.

Given data :

Pencil diameter = 10.5 mm

Length = 14.4 cm = 144 mm

Lead diameter = 1.75 mm

So,

Pencil radius = 10.5/2 = 5.25 mm

Lead radius = 1.75/2 = 0.875 mm

So,

Pencil volume = π × 5.25 ×5.25 × 144 = 22/7 × 5.25 ×5.25 × 144 = 12474 mm³

Lead's volume = π × 0.875 × 0.875 × 144 = 22/7 × 0.875 × 0.875 × 144 = 346.5 mm³

So,wood volume in one pencil = (12474-346.5) = 12127.5 mm³

In 100 pencils = 12127.5 × 100 = 1212750 mm³ = 1212.75 cm³ (answer)