Question

set 5: breaking apart figures to find volume
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: Calculate the volume of the first part of figure 1

The formula for the volume of a rectangular prism is \(V = l\times w\times h\). For the smaller part of figure 1 (with \(l = 12\) ft, \(w = 1\) ft, \(h=3\) ft), \(V_1=1\times3\times(9) = 27\) cubic feet.

Step2: Calculate the volume of the second part of figure 1

For the larger part of figure 1 (with \(l = 12\) ft, \(w = 5\) ft, \(h = 5\) ft), \(V_2=12\times5\times5=300\) cubic feet.

Step3: Find the total volume of figure 1

Add the volumes of the two parts: \(V = V_1+V_2=27 + 300=327\) cubic feet.

Step4: Calculate the volume of the first part of figure 2

For the upper - part of figure 2 (with \(l=(11 - 7)=4\) in, \(w = 4\) in, \(h = 8\) in), \(V_3=4\times4\times8 = 128\) cubic inches.

Step5: Calculate the volume of the second part of figure 2

For the lower - part of figure 2 (with \(l = 11\) in, \(w = 4\) in, \(h=(12 - 8)=4\) in), \(V_4=11\times4\times4=176\) cubic inches.

Step6: Find the total volume of figure 2

Add the volumes of the two parts: \(V=V_3 + V_4=128+176 = 304\) cubic inches.

Answer:

1. \(327\) cubic feet
2. \(304\) cubic inches