Question

This hutch is made up of two rectangular prisms. 1 7 ft 2 ft 2 127 ft 22 ft 4 ft What is the total volume of this hutch, in cubic feet?

Answer 1

40 cubic feet

Explanation

The volume of a rectangular prism is calculated as follows:

`V=whl`

where w is the width, h is the height and l is the length of the prism.

The hutch is made up of two rectangular prisms, one with a width of 1 1/3 ft, a height of 2 1/2 ft, and a length of 4 ft. The other one has a width of 2 2/3 ft, a height of 2 1/2 ft, and a length of 4 ft.

To calculate the volume of the hutch, first, we need to calculate the volume of each prism, and then add them.

The volume of the smaller prism is:

`\begin{gathered} V_1=1(1)/(3)\cdot2(1)/(2)\cdot4 \\ V_1=13(1)/(3)\text{ cubic feet} \end{gathered}`

The volume of the bigger prism is:

`\begin{gathered} V_2=2(2)/(3)\cdot2(1)/(2)\cdot4 \\ V_2=26(2)/(3)\text{ cubic feet} \end{gathered}`

Finally, the volume of the hutch is:

`V_1+V_2=13(1)/(3)+26(2)/(3)=40\text{ cubic feet}`