Curved Surface Area of a Cylinder

A cylindrical soup can has a diameter of 10 cm and a height of 15 cm. A label around the can covers the curved surface area of the can. To calculate this area, we can use the formula for the lateral surface area of a cylinder:

$$ A_{ ext{curved}} = 2 heta r h $$

where $r$ is the radius, $h$ is the height, and $ heta$ is the angle (in radians) that the label covers. In this case, the entire label covers the full 360 degrees, or $2 heta = 2 ext{π}$. Using these values, what is the curved surface area of the can?