Question

the figure represents a water trough in the shape of a rectangular prism. the dimensions of the water trough are given in feet.
water trough
diagram of a rectangular prism with height 4 ft, length 7 ft, and width ( 2\frac{1}{2} ) ft
what is the volume of water in the trough in cubic feet when the trough is full?

Explanation:

Step1: Recall the volume formula for 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: Identify the dimensions

From the problem, the length \( l = 7 \) ft, the width \( w = 2\frac{1}{2} \) ft (which is \( \frac{5}{2} \) ft as an improper fraction), and the height \( h = 4 \) ft.

Step3: Substitute the values into the formula

Substitute \( l = 7 \), \( w = \frac{5}{2} \), and \( h = 4 \) into the volume formula:
\[
V = 7 \times \frac{5}{2} \times 4
\]

Step4: Simplify the expression

First, multiply \( \frac{5}{2} \) and \( 4 \). \( \frac{5}{2} \times 4 = 5 \times 2 = 10 \) (because \( 4 \div 2 = 2 \)). Then multiply this result by 7: \( 7 \times 10 = 70 \).

Answer:

The volume of water in the trough when it is full is \( 70 \) cubic feet.