Question

for the figures in problems 3 - 4, all sides meet at right angles. find the volume of each figure.
3
4

Explanation:

Step1: Divide the composite figure into two rectangular prisms

For the first figure (in cm):

• Prism 1: length \(l_1 = 12\) cm, width \(w_1=12\) cm, height \(h_1 = 4\) cm
• Prism 2: length \(l_2=(12 - 8)=4\) cm, width \(w_2=(12 - 10) = 2\) cm, height \(h_2 = 4\) cm

For the second figure (in ft):

• Prism 1: length \(l_1 = 6\) ft, width \(w_1=6\) ft, height \(h_1 = 4\) ft
• Prism 2: length \(l_2 = 6\) ft, width \(w_2=2\) ft, height \(h_2 = 2\) ft

Step2: Use the volume formula \(V=l\times w\times h\)

• First figure (in cm):
• Volume of Prism 1: \(V_1=12\times12\times4=576\) \(cm^3\)
• Volume of Prism 2: \(V_2 = 4\times2\times4=32\) \(cm^3\)
• Total volume \(V=V_1 + V_2=576+32 = 608\) \(cm^3\)
• Second figure (in ft):
• Volume of Prism 1: \(V_1=6\times6\times4 = 144\) \(ft^3\)
• Volume of Prism 2: \(V_2=6\times2\times2=24\) \(ft^3\)
• Total volume \(V=V_1+V_2=144 + 24=168\) \(ft^3\)

Answer:

The volume of the first figure is \(608\) \(cm^3\) and the volume of the second figure is \(168\) \(ft^3\)