Question

the ratio of the corresponding linear measures of two similar cans of cat food is 4:3. the larger can has a SA of 100 inches. find the surface area of the smaller can. round to the nearest tenth.

Answer 1

56.3 in²

Explanation:

Given 2 similar figures with linear ratio = a : b, then

area ratio = a² : b²

Here linear ratio = 4 : 3, thus

area ratio = 4² : 3² = 16 : 9

Let x be the surface area of the smaller can then by proportion

`(16)/(100)` =
`(9)/(x)` ( cross- multiply )

16x = 900 ( divide both sides by 16 )

x ≈ 56.3 in² ( to the nearest tenth )