Question

name:
figures to find volume
sides meet at right angles. find the volume of
2
4 in.
7 in.
11 in.
8 in.
12 in.
cubic inches
all sides meet at right angles. find the volume of
4
29

Explanation:

Step1: Divide the composite figure into two rectangular prisms

Let's call the lower prism \(P_1\) and the upper prism \(P_2\).
For \(P_1\): length \(l_1 = 8\) in, width \(w_1=4\) in, height \(h_1 = 11-(11 - 7)= 7\) in.
For \(P_2\): length \(l_2=12 - 8 = 4\) in, width \(w_2 = 4\) in, height \(h_2=11\) in.

Step2: Calculate the volume of each prism

The volume formula for a rectangular prism is \(V=l\times w\times h\).
For \(P_1\): \(V_1=l_1\times w_1\times h_1=8\times4\times7 = 224\) cubic inches.
For \(P_2\): \(V_2=l_2\times w_2\times h_2=4\times4\times11=176\) cubic inches.

Step3: Sum the volumes of the two prisms

\(V = V_1+V_2\).
\(V=224 + 176\).

Answer:

\(400\)