Question

The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to roll once over the playground to level. Find the area of the playground in $m^2$.

Answer 1

The roller is in the shape of a cylinder.
Diameter of the roller, d = 84 cm
So, radius of the roller, $r=\frac{d}{2}=42\text{cm}$
Length of the roller = Height of the cylinder, h = 120 cm
1 complete revolution of the roller = Curved surface area of the cylinder
$=2\pi rh$
$=2\times \frac{22}{7}\times 42\times 120c{m}^2$
$=31680c{m}^2$
So, Area covered by the roller in 500 complete revolutions $=31680c{m}^2\times 500$
$=15840000c{m}^2$
1 m = 100 cm
$\text{So},1m^2=1m\times 1m$
$=100\text{cm}\times 100\text{cm}$
$=10000c{m}^2$
Therefore, Area covered by the roller in 500 complete revolutions, in $m^2=\frac{15840000}{10000}=1584m^2$
So, Area of the playground $=1584m^2$