Question

A hollow garden roller, 1 m wide with outside diameter of 30 cm, is made of 2 cm thick iron. Find the volume of the iron. If the roller rolls without sliding for 6 seconds at the rate of 8 complete rounds per second, find the distance travelled and the area covered by the roller in 6 seconds.

Answer 1

Outer dameter of roller = 30cm

Outer radius = `(30)/(2)`
= 15cm
Thickness of iron = 2cm
Length of roller = 1m
= 100cm
Inner radius
= Outer radius - Thickness
= 13cm
Volume of iron
= π{(r_outer)2 - (r_inner)2} x h
= {(15)² - (13)²} x 100
= 17600cm³
∴ The volume of the iron is 17600cm3.    ...(Ans1)
The roller travels 8 round in 1 second,
∴ Total round made in 6seconds 
= 6 x 8
= 48
In one round, distance travelled by roller
= Circumference of the curved surface
∴ Distance travelled in 6seconds
= Circumference x 48
= 2πr_outerx 48
= 4.52m
∴ Distance travelled in 6seconds is 4.52m.  ...(Ans 2)
Area covered in 6second = Distance travelled x Width
Area covered 
= 4.52 x 1
= 4.52m²
∴ The area covered by the roller in 6seconds is 4.52m². ....(Ans 3)