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A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is $ 84 \mathrm{~cm} $ and length is $ 1 \mathrm{~m} $.
Given:
A road roller takes 750 complete revolutions to move once over to level a road.
The diameter of a road roller is \( 84 \mathrm{~cm} \) and length is \( 1 \mathrm{~m} \).
To do:
We have to find the area of the road.
Solution:
Diameter of the road roller$=84\ cm$
Radius of the road roller$=\frac{84}{2}=42\ cm$
Area of the road $=$Number of revolutions $\times$ Area covered in 1 revolution
Area covered in 1 revolution $=$ Lateral surface area of the cylinder
$=2\pi rh$
$=2\times\frac{22}{7}\times\frac{42}{100}\times1$
$=\frac{44\times6}{100}\ m^2$
Area of the road $=750\times\frac{264}{100}\ m^2$
$=15\times132\ m^2$
$=1980\ m^2$
The area of the road is $1980\ m^2$.
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