Question

(from unit 1, lesson 8.) 2. find the volume of the figure. explain or show your reasoning.

Explanation:

Step1: Divide the figure into two rectangular - prisms

We can consider the given figure as composed of two rectangular - prisms. One with dimensions \(5\times3\times2\) and the other with dimensions \(3\times4\times(3 - 2)\).

Step2: Calculate the volume of the first rectangular - prism

The volume formula for a rectangular - prism is \(V = l\times w\times h\). For the first prism with \(l = 5\) in, \(w = 3\) in, and \(h = 2\) in, \(V_1=5\times3\times2= 30\) in³.

Step3: Calculate the volume of the second rectangular - prism

For the second prism with \(l = 3\) in, \(w = 4\) in, and \(h=(3 - 2)=1\) in, \(V_2 = 3\times4\times1=12\) in³.

Step4: Calculate the total volume

The total volume \(V\) of the figure is the sum of the volumes of the two prisms, \(V=V_1 + V_2=30 + 12=42\) in³.

Answer:

42 in³