Question

The thickness of a hollow wooden cylinder is 2 cm. It is 35 cm long and its inner radius is 12 cm. Find the volume of the wood required to make the cylinder assuming it is open at either end.

Answer 1

Given:

Thickness = 2 cm

Length (height) h = 35 cm

Inner radius r = 12 cm (Required: volume of wood for a hollow cylinder open at both ends.)

Outer radius R = r + thickness = 12 + 2 = 14 cm.

Volume of wood = volume of outer cylinder − volume of inner cylinder = π h (R² − r²).

Compute R² − r²

= 14² − 12²

= 196 − 144

= 52

Therefore

V = π × 35 × 52 

= 1820 π cm³

Taking π = `22/7`

gives V = `1820 × 22/7`

= 5720 cm³

Using π ≈ 3.1416

V ≈ 5717.5 cm³.