Question

A rectangular prism has a width of 51 ft and a volume of 144 ft3. Find the volume of a similar prism with a width of 17 ft. Round to the nearest tenth, if necessary.

Answer 1

`5.3\ ft^3`

Explanation:

Similar shapes with scale factor
`k` have proportional volumes with coefficient
`k^3` i.e.

`(V_(large))/(V_(small))=k^3,`

where

`k=\frac{\text{width of large prism}}{\text{width of small prism}}.`

Since

`\text{width of large prism}=51\ ft,\\ \\\text{width of small prism}=17\ ft,`

then

`k=(51)/(17)=3.`

Hence,

`(144)/(V_(small))=3^3\Rightarrow V_(small)=(144)/(27)=(16)/(3)=5(1)/(3)\approx 5.3\ ft^3.`