Question

what is the volume of the rectangular prism? use the formula. 5 yd, 4\frac{2}{3} yd, \frac{3}{4} yd (not drawn to scale). a 13\frac{3}{4} yd³, b 20\frac{1}{2} yd³, c 10\frac{5}{12} yd³, d 17\frac{1}{2} yd³

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular prism is $V = l\times w\times h$, where $l$ is length, $w$ is width and $h$ is height. Here $l = 5$ yd, $w=\frac{3}{4}$ yd and $h = 4\frac{2}{3}$ yd.

Step2: Convert mixed - number to improper fraction

$4\frac{2}{3}=\frac{4\times3 + 2}{3}=\frac{14}{3}$ yd.

Step3: Calculate the volume

$V=5\times\frac{3}{4}\times\frac{14}{3}$. First, simplify the fraction multiplication: $\frac{3}{4}\times\frac{14}{3}=\frac{3\times14}{4\times3}=\frac{14}{4}=\frac{7}{2}$. Then $V = 5\times\frac{7}{2}=\frac{35}{2}=17\frac{1}{2}$ yd³.

Answer:

D. $17\frac{1}{2}$ yd³