The ratio of the corresponding linear measures of two similar cans of fruit is 4 to 7. the smaller can has a surface area of 220 square centimeters. find the surface area of the larger can. write your answer as a decimal or mixed number.

Using the concept of a ratio and proportion to solve the problem. Then the surface area of the larger can is 673.75 square cm.

What are ratio and proportion?

A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Given

The ratio of the corresponding linear measures of two similar cans of fruit is 4 to 7.

The smaller can has a surface area of 220 square centimeters.

Let x be the larger can and y be the smaller can. Then

Then the ratio of their area is given by

Thus, the surface area of the larger can is 673.75 square cm.

More about the ratio and the proportion link is given below.

link

When you have a problem like this one, you have to remember that the linear relationship between the 2 similar objects is one-to-one.  To find the ratio of their areas you have to square each of these one-to-one measures.  If the one-to-one ratio is 4/7, then the ratio of their areas is found by squaring both those numbers to get 16/49.  Obviously 16 is less than 49 so we have our ratio set up with smaller "stuff" on top and larger on bottom.  Work it like a proportion now: where x is the area of the larger object.  Cross-multiply to get 16x = 10780 and x = 673.75.

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What is the inequality?