Question

1. a diagram of a right rectangular prism is shown below. what is the volume of the prism in cubic inches?

8 in.
$1\frac{3}{4}$ in.
$\frac{5}{8}$ in.

Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume \( V \) of a right rectangular prism 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.

Step2: Identify the length, width, and height

From the diagram, we have:

• Length \( l = 8 \) in.
• Width \( w = 1\frac{3}{4} \) in. (which is \( \frac{7}{4} \) in. when converted to an improper fraction)
• Height \( h = \frac{5}{8} \) in.

Step3: Substitute the values into the formula

\[

$$\begin{align*} V&=8\times\frac{7}{4}\times\frac{5}{8}\\ \end{align*}$$

\]
First, simplify \( 8\times\frac{7}{4} \). The 8 and 4 can be simplified: \( 8\div4 = 2 \), so \( 8\times\frac{7}{4}=2\times7 = 14 \). Now we have:
\[

$$\begin{align*} V&=14\times\frac{5}{8}\\ \end{align*}$$

\]
But we can also simplify earlier by canceling the 8 in the numerator and denominator. The 8 in the first term and the 8 in the third term cancel out:
\[

$$\begin{align*} V&=\frac{8}{1}\times\frac{7}{4}\times\frac{5}{8}\\ &=\frac{\cancel{8}}{1}\times\frac{7}{4}\times\frac{5}{\cancel{8}}\\ &=\frac{7}{4}\times5\\ &=\frac{35}{4}\\ & = 8\frac{3}{4} \end{align*}$$

\]

Answer:

The volume of the right rectangular prism is \( 8\frac{3}{4} \) cubic inches (or \( \frac{35}{4} \) cubic inches).