Question

a box in the shape of a rectangular prism has a length of 3\frac{5}{8} inches, a width of 2\frac{1}{2} inches, and a height of 4 inches. what is the volume of the box? 36\frac{1}{4} in.³ 67\frac{1}{8} in.³ 24\frac{5}{16} in.³ 33\frac{9}{16} in.³

Explanation:

Step1: Convert mixed - numbers to improper fractions

$3\frac{5}{8}=\frac{3\times8 + 5}{8}=\frac{29}{8}$, $2\frac{1}{2}=\frac{2\times2+1}{2}=\frac{5}{2}$

Step2: Use volume formula for rectangular prism

The volume $V$ of a rectangular prism is $V = l\times w\times h$. Here, $l=\frac{29}{8}$, $w = \frac{5}{2}$, $h = 4$.
$V=\frac{29}{8}\times\frac{5}{2}\times4$

Step3: Simplify the expression

$V=\frac{29}{8}\times(\frac{5}{2}\times4)=\frac{29}{8}\times10=\frac{29\times10}{8}=\frac{290}{8}=\frac{145}{4}=36\frac{1}{4}\text{ in.}^3$

Answer:

A. $36\frac{1}{4}\text{ in.}^3$