2 m long road roller covers 17.6 m distanc during one revolution. Find its curved surfac area.

To find the curved surface area of a road roller, we can use the formula for the curved surface area of a cylinder, which is given by \( 2\pi rh \), where \( r \) is the radius and \( h \) is the height (or length) of the cylinder. Given that the road roller covers a distance of 17.6 m in one revolution, this distance is the circumference of the roller. We can use the formula for the circumference of a circle: \( C = 2\pi r \). Setting \( C = 17.6 \) m allows us to solve for the radius \( r \): \[ 17.6 = 2\pi r \] \[ r = \frac{17.6}{2\pi} \approx 2.8 \text{ m} \] Now we can calculate the curved surface area: \[ \text{Curved Surface Area} = 2\pi rh \] \[ = 2\pi (2.8)(2) \] \[ \approx 35.2 \text{ m}^2 \] So, the curved surface area of the road roller is approximately 35.2 square meters! For a bit of fun, remember that road rollers aren’t just heavy machinery; they play a vital role in ensuring our roads are flat and smooth. Imagine driving on a bumpy road; without these beasts of compression, we might have quite the rollercoaster experience every time we hit the road!