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 covering the curved surface area of the cylindrical tin, we'll use the formula for the curved surface area (CSA) of a cylinder given by: \[ \text{CSA} = 2\pi rh \] where \( r \) is the radius and \( h \) is the height of the cylinder. 1. **Calculate the radius**: Since the diameter is given as 16 cm, the radius \( r \) is: \[ r = \frac{16}{2} = 8 \text{ cm} \] 2. **Convert the height into an improper fraction**: The height is given as \( 17 \frac{1}{2} \) cm, which is: \[ 17 \frac{1}{2} = \frac{35}{2} \text{ cm} \] 3. **Now substitute the values into the CSR formula**: \[ \text{CSA} = 2\pi (8) \left(\frac{35}{2}\right) \] 4. **Simplify the equation**: \[ \text{CSA} = 2\pi (8) \left(\frac{35}{2}\right) = 8 \times 35 \times \pi = 280\pi \] 5. **Approximate using \( \pi \approx 3.14 \)**: \[ 280\pi \approx 280 \times 3.14 = 879.2 \text{ cm}^2 \] Thus, the area of the label is approximately \( 879.2 \text{ cm}^2 \).