Question

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

Explanation:

Step1: Divide the figure into two rectangular - prisms

We can divide the given L - shaped figure into two rectangular prisms. One prism has dimensions \(10\times7\times(9 - 6)=10\times7\times3\) and the other has dimensions \(10\times6\times1\).

Step2: Use the volume formula for rectangular - prism \(V = l\times w\times h\)

The volume of the first prism \(V_1=10\times7\times3 = 210\) cubic inches. The volume of the second prism \(V_2=10\times6\times1=60\) cubic inches.

Step3: Find the total volume of the figure

The total volume \(V = V_1+V_2\).

Answer:

a. The expression for the volume \(V=10\times7\times(9 - 6)+10\times6\times1\).
b. \(V = 210+60=270\) cubic inches.