How does the original volume of a rectangular prism change when the width is doubled, the length is tripled, and the height is quadrupled?
The equation for the volume of a rectangular prism is:
\(Volume=width\times length\times height\)
If we multiply the width by 2, the length by 3, and the height by 4 in this equation, we have to do the same to the other side so the equation remains true.
\(2\times3\times4\times Volume=(2\times width)\times(3\times length)\times(4\times height)\)
\(24\times Volume=(2\times width)\times(3\times length)\times(4\times height)\)
Therefore the volume will be 24 times it's original value.