Question

determine the volume of the figure in cubic inches. show or explain your thinking.

Explanation:

Step1: Divide the figure into two rectangular - prisms

We can divide the given figure into two rectangular - prisms. One prism has dimensions \(3\times3\times12\) and the other has dimensions \((6 - 3)\times4\times3\).

Step2: Calculate the volume of the first prism

The volume formula for a rectangular - prism is \(V = l\times w\times h\). For the first prism with \(l = 3\) in, \(w = 3\) in, and \(h = 12\) in, \(V_1=3\times3\times12=108\) in³.

Step3: Calculate the volume of the second prism

For the second prism, \(l=(6 - 3)=3\) in, \(w = 4\) in, and \(h = 3\) in. Using the volume formula \(V = l\times w\times h\), we get \(V_2=3\times4\times3 = 36\) in³.

Step4: Calculate the total volume

The total volume \(V\) of the figure is the sum of the volumes of the two prisms. So \(V=V_1 + V_2=108+36 = 144\) in³.

Answer:

144 in³