Question

Two similar geometric solids have a scale factor of 3:4. If the volume of the smaller solid is 54 cubic feet, what is the volume of the larger solid? Round to the nearest tenth as needed.

Thank you for your help!

Answer 1

128 ft³

Explanation:

given the scale factor of 2 similar solids is a : b , then

ratio of volumes = a³ : b³

here a : b = 3 : 4

then 3³ : b³ = 3³ : 4³ = 27 : 64

let x be volume of larger solid then by proportion

`(27)/(54)` =
`(64)/(x)` ( cross- multiply )

27x = 3456 ( divide both sides by 27 )

x = 128

the volume of the larger solid is 128 ft³