Question

a rectangular prism is $11\frac{3}{5}$ meters long, 9 meters wide, and $12\frac{1}{2}$ meters high. what is the volume, in cubic meters, of the prism?

Explanation:

Step1: Recall the formula for the volume of a rectangular prism

The volume \( V \) of a 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: Convert the mixed numbers to improper fractions

• Length \( l = 11\frac{3}{5} = \frac{11\times5 + 3}{5}=\frac{55 + 3}{5}=\frac{58}{5} \) meters.
• Height \( h = 12\frac{1}{2}=\frac{12\times2+ 1}{2}=\frac{24 + 1}{2}=\frac{25}{2} \) meters.
• Width \( w = 9=\frac{9}{1} \) meters.

Step3: Multiply the three dimensions together

\[

$$\begin{align*} V&=\frac{58}{5}\times\frac{9}{1}\times\frac{25}{2}\\ &=\frac{58\times9\times25}{5\times1\times2}\\ &=\frac{58\times9\times5}{1\times1\times2} \quad (\text{since } \frac{25}{5} = 5)\\ &=\frac{58\times45}{2}\\ &= 29\times45 \quad (\text{since } \frac{58}{2}=29)\\ &= 1305 \end{align*}$$

\]

Answer:

The volume of the rectangular prism is \( 1305 \) cubic meters.