Question

The student council memebers are making decorative labels to cover 20 identical empty coffee cans for charity drive. Each label will cover the entire lateral surface area of a can. Which is the closest to the lateral surface coffee can

Answer 1

Answer:

• 127.48 in²

Explanation:

The image attached shows the dimensions of the coffe cans considered for this question.

The figure is a cylinder with dimensions:

• $\text {radius }3\frac{1}{16}\text {inches and height }6\frac{5}{8}\text {inches}$

Thus, to find the lateral surface of a coffe can, you use the formula for the lateral area of a cylinder:

• $LA=2\pi\times r\times h$

Where, LA is the lateral area, r is the radius, and h is the height.

Substituting the dimensions given in the figure, you get:

• $LA=2\pi\times 3\frac{1}{16}\times 6\frac{5}{8}$

To multiply, first convert the mixed numbers into improper fractions:

$3\frac{1}{16}=3+\frac{1}{16}=\frac{3(16)+1}{16}=\frac{48+1}{16}=\frac{49}{16}\\ \\ 6\frac{5}{8}=6+\frac{5}{8}=\frac{6(8)+5}{8}=\frac{48+5}{8}=\frac{53}{8}$

Now, you can multiply:

• $LA=2\pi\times \frac{49}{16}\times \frac{53}{8}$

• $LA=127.48in^2$