A paper label just covers the curved surface area of a cylindrical tin of diameter 16 cm and height \( 17 \frac{1}{2} \mathrm{~cm} \). Calculate the area of the label.

To calculate the area of the label that covers the curved surface area of the cylindrical tin, we need to find the curved surface area of the cylinder first. The formula for the curved surface area of a cylinder is given by: \[ \text{Curved Surface Area} = 2 \pi r h \] where: - \( r \) is the radius of the cylinder - \( h \) is the height of the cylinder Given: - Diameter of the cylinder = 16 cm - Height of the cylinder = \( 17 \frac{1}{2} \) cm First, let's find the radius of the cylinder: \[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{16}{2} = 8 \, \text{cm} \] Now, we can calculate the curved surface area of the cylinder: \[ \text{Curved Surface Area} = 2 \pi \times 8 \times 17.5 \] Let's calculate the curved surface area. Calculate the value by following steps: - step0: Calculate: \(2\pi \times 8\times 17.5\) - step1: Multiply the terms: \(280\pi \) The curved surface area of the cylindrical tin is approximately 879.65 cm². Therefore, the area of the label that covers the curved surface area of the cylindrical tin is approximately 879.65 cm².