Question

A road roller of length 3`l`m and radius `l/3` m can cover field in 100 revolutions moving once over. The area of the field in terms of `l` ......... m²

Curved surface area = 2πrh

h = `square` m

`square = l/3` m

∴ Curved surface area of cylinder = `square` × 2

∴ Area of field = 2πrl² × 100 = `square`

Answer 1

1. Identify given values

Length/Height (h): 3`l` m

Radius (r): `l/3` m

2. First box (h):

h = \[\boxed{3l}\] m

Second box (Variable identification):

\[\boxed{r} = \frac{l}{3} m\]

Third box (Curved surface area calculation):

Curved surface area = 2 × π × r × h

= `2 xx π xx l/3 xx 3l`

= 2π`l`²

Since it is formatted as [Box] × 2:

∴ Curved surface area of cylinder = \[\boxed{πl^2} \times 2\]

Fourth box (Total area of the field):

The roller makes 100 revolutions to cover the field.

Area of field = 2π`l`² × 100

= \[\boxed{200πl^2} \phantom{.} m^2\]