Question

what is the volume of this figure? 4 in. 7 in. 11 in. 4 in. 13 in. cubic inches

Explanation:

Step1: Divide the figure into two rectangular - prisms

We can divide the given figure into two rectangular - prisms. One prism has dimensions \(4\times4\times11\) and the other has dimensions \(4\times7\times13 - 11=2\).

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 \(l = 4\), \(w = 4\), and \(h = 11\), \(V_1=4\times4\times11 = 176\) cubic inches.

Step3: Calculate the volume of the second prism

For the second prism with \(l = 4\), \(w = 7\), and \(h = 2\), \(V_2=4\times7\times2=56\) cubic inches.

Step4: Calculate the total volume

The total volume \(V = V_1 + V_2\). So \(V=176 + 56=232\) cubic inches.

Answer:

232