Question

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

Answer 1

Given: Diameter of the roller $=84cm$

$\therefore$ Radius(r) $=\frac{84}{2}=42cm$ and length $\left(h\right)=120cm$

$\therefore$ Curved surface area of the cylindrical roller $=2\pi rh$

$=2\times \frac{22}{7}\times 42\times 120c{m}^2$

$=31680c{m}^2=\frac{31680}{10000}{m}^2=3.168m^2$ [$\because 1m=100cm$ ]

Area covered in $1$ revolution $=$ Curved surface area of the cylindrical roller $=3.168m^2$

Area covered in $500$ complete revolutions $=3.168\times 500m^2=1584m^2$

$\therefore$ Area of the playground $=$ Area covered in $500$ complete revolutions $=1584m^2$