Question

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

• A. $1584m^2$
• B. $1284m^2$
• C. $1554m^2$
• D. none of the above

Answer 1

The correct option is A $1584m^2$

The roller is in the shape of a cylinder.
Since
the diameter of the roller is $84cm$, its radius is $42cm$.
In one revolution, the wheel covers the distance of its one curved surface area
Curved
Surface Area of a Cylinder of Radius "R" and height "h" $=2\pi Rh$
Hence, area of the playground covered in one revolution $=2\times \frac{22}{7}\times 42\times 120=31680sqcm$
Area of playground $=$ Distance covered in $500$ revolutions $=500\times 31680=15840000sqcm$ or $1584sqm$