Question

a. write an expression to represent the volume of the figure in cubic inches.
b. find the volume of the figure

Explanation:

Step1: Analyze the figure as two - part

The figure can be seen as two rectangular prisms. One has dimensions \(10\times7\times(9 - 6)\) and the other has dimensions \(10\times7\times6\).

Step2: Write the volume formula for the combined figure

The volume \(V\) of the combined figure is \(V=10\times7\times(9 - 6)+10\times7\times6\).

Step3: Simplify the expression

First, calculate \(10\times7\times(9 - 6)=10\times7\times3 = 210\). Then, calculate \(10\times7\times6=420\). Add them together: \(V=210 + 420=630\).

Answer:

a. The expression for the volume is \(10\times7\times(9 - 6)+10\times7\times6\).
b. The volume of the figure is \(630\) cubic inches.