Question

draw line(s) to show how you decomposed the figure. what is the volume of the figure? 6. 5 ft 3 ft 2 ft 2 ft 2 ft 2 ft 7. 2 in. 5 in. 5 in. 5 in. 5 in. 5 in. 10 in. 8. stem connection an ocean engineer is designing an underwater robot. the robot will have two pieces like the one shown. what is the volume of the robot? 9. a sign company made this letter using rectangular prisms. each prism is 12 inches by 4 inches by 4 inches. what is the volume of the letter? explain.

Explanation:

Step1: Decompose the first - figure

The first figure can be decomposed into two rectangular prisms. One prism has dimensions \(l = 5\) ft, \(w=2\) ft, \(h = 5\) ft and the other has dimensions \(l = 5\) ft, \(w = 2\) ft, \(h=3\) ft.

Step2: Calculate the volume of the first part of the first - figure

The volume formula for a rectangular prism is \(V=l\times w\times h\). For the first part with \(l = 5\) ft, \(w = 2\) ft, \(h = 5\) ft, \(V_1=5\times2\times5= 50\) cubic - feet.

Step3: Calculate the volume of the second part of the first - figure

For the second part with \(l = 5\) ft, \(w = 2\) ft, \(h = 3\) ft, \(V_2=5\times2\times3 = 30\) cubic - feet.

Step4: Find the total volume of the first - figure

\(V_{total1}=V_1 + V_2=50+30 = 80\) cubic - feet.

Step5: Decompose the second - figure

The second figure can be decomposed into three rectangular prisms. The bottom prism has dimensions \(l = 10\) in, \(w = 5\) in, \(h = 5\) in, the middle prism has dimensions \(l = 5\) in, \(w = 5\) in, \(h = 5\) in, and the top prism has dimensions \(l = 5\) in, \(w = 2\) in, \(h = 5\) in.

Step6: Calculate the volume of the bottom part of the second - figure

Using \(V=l\times w\times h\), for the bottom part with \(l = 10\) in, \(w = 5\) in, \(h = 5\) in, \(V_3=10\times5\times5 = 250\) cubic - inches.

Step7: Calculate the volume of the middle part of the second - figure

For the middle part with \(l = 5\) in, \(w = 5\) in, \(h = 5\) in, \(V_4=5\times5\times5=125\) cubic - inches.

Step8: Calculate the volume of the top part of the second - figure

For the top part with \(l = 5\) in, \(w = 2\) in, \(h = 5\) in, \(V_5=5\times2\times5 = 50\) cubic - inches.

Step9: Find the total volume of the second - figure

\(V_{total2}=V_3+V_4 + V_5=250+125 + 50=425\) cubic - inches.

Answer:

The volume of the first figure is 80 cubic - feet and the volume of the second figure is 425 cubic - inches.