The length of a box is reduced to two third of its original value and the width and height are tripled. Calculate the factor by which the volume has changed.
Am I on the right track? If not please help I am stuck. Thanks.
V=LWH
V=(L-2/3)(3W)(3H)
(2L/3)(3W)(3H)
To calculate the factor by which the volume has changed, we need to compare the new volume (V') with the original volume (V).
Let's start by substituting the values into the formula you provided:
V' = (L - 2/3)(3W)(3H)
Next, let's expand the expression:
V' = (3L/3 - 2/3)(3W)(3H)
V' = (3L - 2/3)(3W)(3H)
V' = (9L - 2)(3W)(3H)
V' = 27LWH - 6WH
Now, we can calculate the factor by which the volume has changed:
Factor = (V' - V) / V
Factor = (27LWH - 6WH - LWH) / LWH
Factor = (26LWH - 6WH) / LWH
Factor = 26 - (6WH / LWH)
Factor = 26 - (6W / L)
Since the width of the box has tripled, we can substitute the new value:
Factor = 26 - (6 * 3 / L)
Factor = 26 - (18 / L)
Factor = 26L/L - 18 / L
Factor = (26L - 18) / L
Therefore, the factor by which the volume has changed is given by (26L - 18) / L.