Question

A rectangular prism has dimensions of 2 ft, 4 ft, and 6 ft. If the dimensions are doubled, what would happen to the volume?

Answer 1

Volume is increased in a factor of 8. The volume is increased from
`48\,ft^(3)` to
`384\,ft^(3)`.

Explanation:

The formula for the volume of the rectangular prism is:

`V = w\cdot h \cdot l`

Where:

`w` - Width

`h` - Height

`l` - Length

If dimensions are doubled, then volume is increased in a factor of 8:

`V_(f) = (2\cdot w)\cdot (2\cdot h)\cdot (2\cdot l)`

`V_(f) = 8\cdot w \cdot h \cdot l`

`V_(f) = 8 \cdot V_(o)`

The volume is increased from
`48\,ft^(3)` to
`384\,ft^(3)`.