A road roller of diameter 2.24 m and length 1 m has to press a ground of area 880 m². How many revolutions does it make to complete the work?

The correct option is 125.

To find the total number of revolutions the road roller makes to press the given ground area, we need to calculate the curved surface area (CSA) pressed by the roller in one single revolution.

Step 1: Identify the given dimensions of the road roller

Diameter of the roller ($d$) = 2.24 m
Radius of the roller ($r$) = $\frac{2.24}{2}=1.12$ m
Length (or height, $h$) of the roller = 1 m
Total area of the ground to be pressed = 880 m²

Step 2: Calculate the area covered in one revolution

The area covered by the roller in one complete revolution is equal to its curved surface area (CSA).

$CSA=2\pi rh$

Using $\pi =\frac{22}{7}$:

$Area\; in\; 1\; revolution=2\times \frac{22}{7}\times 1.12\times 1$

$Area\; in\; 1\; revolution=2\times 22\times 0.16\times 1=7.04$ m²

Step 3: Calculate the total number of revolutions

The total number of revolutions required is given by:

$Number\; of\; revolutions=\frac{\text{Total Area of Ground}}{\text{Area covered in 1 revolution}}$

$Number\; of\; revolutions=\frac{880}{7.04}=125$

Thus, the road roller makes 125 revolutions to press the ground completely.