To calculate the area covered by the roller, we need to consider the surface area that the roller traverses as it makes 25 revolutions. The roller can be thought of as unrolling into a flat strip of paper. The length of this strip would be equal to the distance the roller travels in one revolution, and the width would be the circumference of the roller.
Given:
- Diameter of the roller = 14 cm
- Length of the roller = 7 cm
- Number of revolutions = 25
First, let's find the circumference of the roller:
Circumference = π × diameter
Circumference = 3.14159 × 14 cm
Circumference ≈ 43.9823 cm
The distance the roller travels in one revolution is equal to its circumference.
Now, let's calculate the total distance the roller travels in 25 revolutions:
Total distance = Circumference × Number of revolutions
Total distance = 43.9823 cm × 25 revolutions
Total distance = 1099.5575 cm
Now we need to calculate the area covered by the unrolled strip of length 1099.5575 cm and width 7 cm (which is the length of the roller):
Area = Length × Width
Area = 1099.5575 cm × 7 cm
Area = 7696.9025 square cm
So, the roller covers an area of approximately 7696.9025 square cm when it makes 25 revolutions.