Question

set 5: breaking apart figures to find volume
name:
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: Dimensions \(12\times5\times3\)
• Prism 2: Dimensions \(9\times5\times1\)

For problem 2:

• Prism 1: Dimensions \(8\times(11 - 7)\times(12 - 4)\)
• Prism 2: Dimensions \(7\times11\times4\)

Step2: Calculate the volume of each prism using the formula \(V=l\times w\times h\)

For problem 1:

• Volume of Prism 1: \(V_1=12\times5\times3 = 180\) cubic feet
• Volume of Prism 2: \(V_2=9\times5\times1=45\) cubic feet
• Total volume \(V = V_1+V_2=180 + 45=225\) cubic feet

For problem 2:

• Volume of Prism 1: \(V_1=8\times4\times8=256\) cubic inches
• Volume of Prism 2: \(V_2=7\times11\times4 = 308\) cubic inches
• Total volume \(V=V_1 + V_2=256+308 = 564\) cubic inches

Answer:

1. \(225\) cubic feet
2. \(564\) cubic inches