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. Find the area of the playground in $m^2$.

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

Answer 1

The correct option is A

$1584m^2$

Explanation for the correct option:

Step 1.Finding radius of roller

Diameter of roller $=84cm$

Therefore radius $\left(r\right)=\frac{84}{2}=42cm$

Step 2.Finding $CSA$ of roller.

$CSA$ of roller $=CSA$ of cylinder

$$\begin{gathered} =2\mathrm{\pi rh} \\ =2\mathrm{x}\frac{22}{7}\mathrm{x}42\mathrm{x}120\mathbf{[}\mathbf{}\mathbf{given}\mathbf{}\mathbf{,}\mathbf{h}\mathbf{=}\mathbf{120}\mathbf{}\mathbf{cm}\mathbf{]} \\ =44\mathrm{x}6\mathrm{x}120 \\ =44\mathrm{x}720 \\ =31680{\mathrm{cm}}^2 \end{gathered}$$

Step 2.Finding area of playground

Area covered by roller in one revolution $=31680c{m}^2$

Therefore area covered by roller in $500$ revolution$=\frac{500x31680}{10000}\mathbf{}\mathbf{[}\mathbf{}\mathbf{1}\mathbf{}{\mathbf{cm}}^{\mathbf{2}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{10000}}\mathbf{}{\mathbf{m}}^{\mathbf{2}}]$

$=1584m^2$

Area of the playground $=$area covered by roller in $500$ revolution

$=1584m^2$

Hence option (A) is the correct option.