A can of baked beans has a paper label wrapped around the outside. The can has a height of 11cm and radius of4.5cm. The label covers the entire height of the can. The label has a 1cm overlap vertically so that it can bestuck together Calculate the area of the label.
Question
A can of baked beans has a paper label wrapped around the outside. The can has a height of 11cm and radius of4.5cm. The label covers the entire height of the can. The label has a 1cm overlap vertically so that it can bestuck together Calculate the area of the label.
Solution 1
To calculate the area of the label, we need to find the lateral surface area of the cylinder (the can) and add the area of the overlap.
Step 1: Calculate the lateral surface area of the cylinder The formula for the lateral surface area of a cylinder is 2πrh, where r is the radius and h is the height.
So, the lateral surface area = 2π * 4.5cm * 11cm = 297 cm²
Step 2: Calculate the area of the overlap The overlap is a rectangle with dimensions 1cm by 11cm.
So, the area of the overlap = 1cm * 11cm = 11 cm²
Step 3: Add the two areas together Total area of the label = lateral surface area + area of overlap = 297 cm² + 11 cm² = 308 cm²
So, the area of the label is 308 cm².
Solution 2
To calculate the area of the label, we need to find the lateral surface area of the cylinder (the can) and add the area of the overlap.
Step 1: Calculate the lateral surface area of the cylinder. The formula for the lateral surface area of a cylinder is 2πrh, where r is the radius and h is the height.
So, the lateral surface area = 2π * 4.5cm * 11cm = 297 cm².
Step 2: Calculate the area of the overlap. The overlap is a rectangle with dimensions 1cm by the circumference of the can (which is the length of the label before it's wrapped around the can). The formula for the circumference of a circle is 2πr.
So, the length of the label = 2π * 4.5cm = 28.27 cm.
Therefore, the area of the overlap = 1cm * 28.27cm = 28.27 cm².
Step 3: Add the lateral surface area of the cylinder and the area of the overlap to get the total area of the label.
So, the total area of the label = 297 cm² + 28.27 cm² = 325.27 cm².
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