Choose the one alternative that best completes the statement or answers the question.
-If the height of a rectangular solid is held constant, the volume varies jointly with the length and the width. If the volume is 160 cubic inches when the length is 8 inches and the width is 5 inches, find the volume when the length is 7 inches and the width is 6 inches.
A) 140 in. ${ }^{3}$
B) 168 in. ${ }^{3}$
C) 126 in..$^{3}$
D) 192 in. ${ }^{3}$

Question

Quizplus · Accepted Answer

The volume of a rectangular solid is given by the formula $V = l \times w \times h$, where $l$ is the length, $w$ is the width, and $h$ is the height. Since the height is constant, the volume varies directly with the product of the length and width. Given $V_1 = 160$ when $l_1 = 8$ and $w_1 = 5$, and asked for $V_2$ when $l_2 = 7$ and $w_2 = 6$, we can set up a proportion based on the direct variation: $\frac{V_1}{l_1 \times w_1} = \frac{V_2}{l_2 \times w_2}$. Substituting the given values, we find $V_2 = \frac{160}{8 \times 5} \times 7 \times 6 = 168$ cubic inches.

Choose the One Alternative That Best Completes the Statement or Answers