A rectangular prism has dimensions /, w, and h. If the width is changed to 2w and the length is changed to 0.51, how much does the volume change?
The original volume of the rectangular prism is V = lwh.
If the width is changed to 2w, the new volume becomes V' = (0.51)(2w)(h).
The percentage change in volume is given by (V' - V)/V * 100%.
Substituting the expressions for V and V', we have ((0.51)(2w)(h) - lwh)/lwh * 100%.
Simplifying this expression gives ((0.51)(2w)(h) - lwh)/lwh * 100% = ((0.51)(2w)(h) - (w)(h))/lwh * 100%.
Further simplification gives ((1.02)(w)(h) - (w)(h))/lwh * 100%.
Factoring out (w)(h) from the numerator gives ((w)(h)((1.02) - 1))/lwh * 100%.
Simplifying further gives (w)(h)(0.02)/lwh * 100% = 0.02 * 100% = 2%.
Therefore, the volume changes by 2%.