Question

the... water trough in the shape of a rectangular prism. the dimensions of the water trough are shown in the... water trough diagram with 4 ft, 7 ft, 2 3/5 ft. what is the volume of water in the trough in cubic feet when the trough is full? options a and b with fractions, radio buttons a and b

Explanation:

Step1: Identify the formula for volume of a rectangular prism

The volume \( V \) of a rectangular prism (which the water trough appears to be) 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: Extract the dimensions from the problem

From the diagram, the length \( l = 7\) ft, the width \( w = 2\frac{3}{5}\) ft (which is \( \frac{13}{5}\) ft as an improper fraction), and the height \( h = 4.8\) ft (which is \( \frac{24}{5}\) ft as a fraction since \( 4.8=\frac{48}{10}=\frac{24}{5}\)).

Step3: Substitute the values into the volume formula

\[

$$\begin{align*} V&=7\times\frac{13}{5}\times\frac{24}{5}\\ &=7\times\frac{13\times24}{5\times5}\\ &=7\times\frac{312}{25}\\ &=\frac{2184}{25}\\ & = 87.36 \end{align*}$$

\]
Wait, maybe the dimensions are \( l = 7\) ft, \( w = 2\frac{3}{5}\) ft, \( h = 4.8\) ft. Let's check the mixed numbers. Wait, maybe the options are in mixed numbers. Let's re - express \( 4.8\) as a mixed number: \( 4.8 = 4\frac{4}{5}=\frac{24}{5}\), \( 2\frac{3}{5}=\frac{13}{5}\)

\[

$$\begin{align*} V&=7\times2\frac{3}{5}\times4.8\\ &=7\times\frac{13}{5}\times\frac{24}{5}\\ &=\frac{7\times13\times24}{25}\\ &=\frac{7\times312}{25}\\ &=\frac{2184}{25}\\ & = 87\frac{9}{25}? \end{align*}$$

\]
Wait, maybe I misread the dimensions. Let's assume the dimensions are length \( l = 7\) ft, width \( w = 2\frac{3}{5}\) ft, height \( h = 4.8\) ft. Let's convert \( 2\frac{3}{5}\) to decimal: \( 2\frac{3}{5}=2.6\)

Then \( V=7\times2.6\times4.8\)

First, \( 7\times2.6 = 18.2\)

Then \( 18.2\times4.8=87.36\) cubic feet.

But the options are in mixed numbers. Let's check the options again. The first option is \( 87\frac{9}{25}\) (since \( \frac{9}{25}=0.36\)) and \( 87\frac{9}{25}=87.36\), the second option is \( 2\frac{1}{5}\) which is 2.2, which is too small. So the correct option should be A.

Answer:

A. \( 87\frac{9}{25}\text{ ft}^3\)