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

$(\frac{2}{3})^2 = \frac{4}{9}$

Therefore, area and above ratio is in proportion

$\frac{4}{9} = \frac{180}{x}\\\\4x = 180 \times 9\\\\4x = 1620\\\\x = 405$

Thus surface area of the larger can is 405 square centimeter