Word Problem

Question

a popular brand of soup comes in cans that are 2 5/8 inches in diameter and 3 3/4 inches tall. each such can has a paper label that covers the entire side of the can. If you remove the label from a soup can, you'll see that it's made from a rectangular piece of paper. how wide and how long is this rectangle?

Answer 1

It is a an approximation, but you may estimate π as 22/7.

 

The height of the can (and of the removed label) is:

     3 3/4 inches

 

The with of the label (also the circumference of the can, which is π*d), is:

    (22/7) * (2 5/8)

     (22/7) * (21/8)

       (11) * (3/4)

           33/4

           8 1/4 inches

 

     [note: using π=3.1415926 and d=2.625 gives 8.246681]

 

The dimensions of the label are:

     3 3/4 inches  by  8 1/4 inches

 

[Note: since the dimensions of the can are given as improper fractions (2 5/8 inches in diameter and 3 3/4 inches tall, it makes a lot of sense to present the answer using improper fractions.  Why this pressure to change to decimal values (my ruler doesn't measure them)?] 

Answer 2

The dimensions of the rectangle are the same as the height and circumference of the can.

The height of the can is 3.75 inches.

The circumference of the can is π(2.625) or 8.245 inches. 

Answer 3

OK. If there's no part of the can left uncovered, and no overlap on the label, then the label's dimensions are (can height) x (can circumference).

 

The height is given. The circumference is π times diameter. Calculate that and you're done! Cheers!