Question

set 5: breaking apart figures to find volume
name: raquel boy
for the figures in problems 1 - 2, all sides meet at right angles. find the volume of each figure. show your work.
1
2

Explanation:

Step1: Divide the figure into two rectangular prisms

For problem 1:

• Prism 1: length \(l_1 = 9\) ft, width \(w_1=3\) ft, height \(h_1 = 1\) ft.
• Prism 2: length \(l_2 = 12\) ft, width \(w_2 = 5\) ft, height \(h_2=1\) ft.

For problem 2:

• Prism 1: length \(l_1 = 8\) in, width \(w_1=(12 - 4)=8\) in, height \(h_1=(11 - 7) = 4\) in.
• Prism 2: length \(l_2 = 4\) in, width \(w_2 = 12\) in, height \(h_2=7\) in.

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

For problem 1:

• Volume of Prism 1: \(V_1=9\times3\times1=27\) cubic feet.
• Volume of Prism 2: \(V_2=12\times5\times1 = 60\) cubic feet.

For problem 2:

• Volume of Prism 1: \(V_1=8\times8\times4=256\) cubic inches.
• Volume of Prism 2: \(V_2=4\times12\times7=336\) cubic inches.

Step3: Sum the volumes of the prisms

For problem 1: \(V = V_1+V_2=27 + 60=87\) cubic feet.
For problem 2: \(V=V_1 + V_2=256+336 = 592\) cubic inches.

Answer:

1. \(87\) cubic feet
2. \(592\) cubic inches