Question

what is the volume of the following rectangular prism?3 1/31 2/5

Answer 1

The volume (V) of the given prism will be equal to the area of the green zone times the lenght of 1 2/5 units, that is,

$\begin{gathered} V=\text{ gre}en\text{ zone area }\times\text{ lenght} \\ V=3\frac{1}{3}\times1\frac{2}{5}units^3 \end{gathered}$

In order to make the product of the mixed fractions, we need to convert them into simple fraction form, that is,

$\begin{gathered} 3\frac{1}{3}=\frac{3\times3+1}{3}=\frac{10}{3} \\ 1\frac{2}{5}=\frac{5\times1+2}{5}=\frac{7}{5} \end{gathered}$

Then, the volume is given as

$\begin{gathered} V=\frac{10}{3}\times\frac{7}{5} \\ V=\frac{10\times7}{3\times5} \\ V=\frac{70}{15} \\ V=\frac{14}{3} \end{gathered}$

Then, the volume expressed in simple fraction form is:

$V=\frac{14}{3}\text{ cubic u nits}$

In order to convert this result into mixed form, we need to find the following division:

Then, the answer in mixed form is:

$V=4\frac{2}{5}\text{ cubic units}$