Question

A cylindrical road roller made up of iron is 1 m wide. Its inner diameter is 54 cm and thickness of the iron sheet rolled into the road roller is 9 cm. Find the weight of the roller if 1 cm³ of iron weighs 8 g.

Answer 1

Given:

Width (height) of roller,

h = 1 m = 100 cm

Inner diameter = 54 cm

⇒ Inner radius,

r = 27 cm

Thickness of iron sheet = 9 cm

⇒ Outer radius,

R = 27 + 9 = 36 cm

Weight of iron = 8 g per cm³

Volume of iron used (hollow cylinder):

V = πh(R² − r²)

= `22/7 xx 100 xx (36^2 − 27^2)`

= `22/7 xx 100 xx (1296 − 729)`

= `22/7 xx 100 xx 567`

= 178200 cm³

Weight of the roller:

= 178200 × 8

= 1425600 g

= 1425.6 kg

The weight of the road roller is 1425.6 kg.