Question

If prism A and Prism B have a ratio of similarity of 2:3, what is the volume of prism A if Prism B's volume is 56 cubic inches

Answer 1

16.6 in³

Explanation:

Given the ratio of similarity = 2 : 3, then

the ratio of volumes = 2³ : 3³ = 8 : 27

let the volume of prism A be x then by proportion

`(x)/(8)` =
`(56)/(27)` ( cross- multiply )

27x = 448 ( divide both sides by 27 )

x = 448 ÷ 27 ≈ 16.6 ( to 1 dec. place )

Prism A has a volume of approx 16.6 in³