Question

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

Explanation:

Step1: Divide the figure into two rectangular prisms

For problem 3:

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

For problem 4:

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

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

Problem 3:

• Volume of Prism 1: \(V_1=l_1\times w_1\times h_1=12\times10\times4 = 480\) \(cm^3\)
• Volume of Prism 2: \(V_2=l_2\times w_2\times h_2=4\times12\times4=192\) \(cm^3\)
• Total volume \(V = V_1+V_2=480 + 192=672\) \(cm^3\)

Problem 4:

• Volume of Prism 1: \(V_1=l_1\times w_1\times h_1=6\times6\times4 = 144\) \(ft^3\)
• Volume of Prism 2: \(V_2=l_2\times w_2\times h_2=2\times6\times2 = 24\) \(ft^3\)
• Total volume \(V=V_1 + V_2=144+24 = 168\) \(ft^3\)

Answer:

Problem 3: \(672\) \(cm^3\)
Problem 4: \(168\) \(ft^3\)