Question

what is the volume of this figure? cubic centimeters

Explanation:

Step1: Divide the figure into two rectangular - prisms

We can consider the figure as composed of two rectangular - prisms. One has dimensions \(7\ cm\times6\ cm\times1\ cm\) and the other has dimensions \(3\ cm\times6\ cm\times2\ cm\).

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 \(l = 7\ cm\), \(w = 6\ cm\), and \(h = 1\ cm\), \(V_1=7\times6\times1 = 42\ cm^3\).

Step3: Calculate the volume of the second rectangular - prism

For the second prism with \(l = 3\ cm\), \(w = 6\ cm\), and \(h = 2\ cm\), \(V_2=3\times6\times2=36\ cm^3\).

Step4: Calculate the total volume of the figure

The total volume \(V = V_1 + V_2\). So \(V=42 + 36=78\ cm^3\).

Answer:

78