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

• 127.48 in²

Step-by-step 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(1)/(16)\text {inches and height }6(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* r* 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* 3(1)/(16)* 6(5)/(8)`

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

`3(1)/(16)=3+(1)/(16)=(3(16)+1)/(16)=(48+1)/(16)=(49)/(16)\\ \\ 6(5)/(8)=6+(5)/(8)=(6(8)+5)/(8)=(48+5)/(8)=(53)/(8)`

Now, you can multiply:

• 
  `LA=2\pi* (49)/(16)* (53)/(8)`

• 
  `LA=127.48in^2`