Question

A Koi pond is in the shape of a right rectangular prism that is 2 1/2 yd Long, 3 yd wide, and 2 Yd high. The pond is 1/3 full of water. What is the volume of the water in the pond?

Answer 1

The volume of any rectangular prism is

$V=L\times W\times H$

L is the length

W is the width

H is the height

To find the volume of the water in the pond, we will use its length and its width, but we will use 1/3 of its height because the height of the water is 1/3 of the height of the pond

$\begin{gathered} L=2\frac{1}{2} \\ W=3 \\ H=\frac{1}{3}\times2=\frac{2}{3} \end{gathered}$

Now let us substitute them in the rule above

$\begin{gathered} V=2\frac{1}{2}\times3\times\frac{2}{3} \\ V=\frac{2\times2+1}{2}\times3\times\frac{2}{3} \\ V=\frac{5}{2}\times3\times\frac{2}{3} \end{gathered}$

3 up will cancel 3 down and 2 up will cancel 2 down, then

$\begin{gathered} V=5\times1\times1 \\ V=5yd^2 \end{gathered}$

The volume of the water is 5 square yards

$2\frac{1}{2}=\frac{2\times2+1}{2}=\frac{4+1}{2}=\frac{5}{2}$