A lead pencil is in the shape of right circular cylinder. The pencil is 28 cm long and its radius is 3 mm. If the lead is of radius 1 mm, then find the volume of the wood used in the pencil.

GIVEN :

inner diameter of the cylinder of lead “r” = 1mm = 0.1cm

height of the pencil “h” = 28cm

outer radius of the pencil “R” = 3mm = 0.3cm

we take π =

TO FIND : volume of the wood used in the pencil “V” = ?

PROCEDURE :

Here, we will use the concept of hollow cylinder.

So, volume of the wood used in the pencil,

“V” = π × h× (R + r )× (R – r)

So, we put all the values in the above formula, and get

V = × 28 × (0.3 + 0.1)× (0.3 - 0.1)

= 22 × 4 × (0.4)× (0.2)

= 22 × 4 × 4 × 2 × 10^-2

= 704 × 10^-2

= 7.04 cm³

∴ volume of the wood used in the pencil is 7.04 cm³