Question

The ratio of the corresponding linear measures of two similar cans of vegetables is 2 to 3. The smaller can has a surface area of 180 square centimeters. Find the surface area of the larger can.

Answer 1

The surface area of the larger can is 405 square centimeter

Solution:

The ratio of the corresponding linear measures of two similar cans of vegetables is 2 to 3

The smaller can has a surface area of 180 square centimeters

Let the surface area of larger can be "x"

Area is a square measurement

Therefore to find the ratio of the areas, we need to square the ratio of the linear measurements

`((2)/(3))^2 = (4)/(9)`

Therefore, area and above ratio is in proportion

`(4)/(9) = (180)/(x)\\\\4x = 180 * 9\\\\4x = 1620\\\\x = 405`

Thus surface area of the larger can is 405 square centimeter