Questions: Meghan is completing a craft project that involves covering only the lateral surface of a cylindrical container with fabric. The cylinder has a height of 12.9 in and a radius of 13.6 in. To the nearest square unit how much fabric does she need for this project? Use a calculator. 1,683 in ^2 1,102 in. ^2

Solution Steps

To find the amount of fabric needed to cover the lateral surface of a cylindrical container, we need to calculate the lateral surface area of the cylinder. The formula for the lateral surface area of a cylinder is given by:

\[ \text{Lateral Surface Area} = 2 \pi r h \]

where \( r \) is the radius and \( h \) is the height of the cylinder. Given the height \( h = 12.9 \) inches and the radius \( r = 13.6 \) inches, we can plug these values into the formula to find the lateral surface area.

We are given the height and radius of the cylindrical container:

• Height, \( h = 12.9 \) inches
• Radius, \( r = 13.6 \) inches

The formula for the lateral surface area of a cylinder is: \[ \text{Lateral Surface Area} = 2 \pi r h \]

Substituting \( r = 13.6 \) and \( h = 12.9 \) into the formula: \[ \text{Lateral Surface Area} = 2 \pi (13.6) (12.9) \]

Perform the calculation: \[ \text{Lateral Surface Area} = 2 \pi (13.6) (12.9) \approx 2 \times 3.1416 \times 13.6 \times 12.9 \approx 1102.3220 \]

Rounding the result to the nearest square unit: \[ \text{Lateral Surface Area} \approx 1102 \]

Final Answer