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 5 ft 7. 2 in. 5 in. 5 in. 5 in. 5 in. 5 in. 10 in. 5 in.

Explanation:

Step1: Decompose the first figure

The first figure can be decomposed into three rectangular - prisms. Two vertical prisms with dimensions \(2\times3\times5\) and one horizontal prism with dimensions \((2 + 2+2 + 2)\times(5 - 3)\times5\).
The volume formula for a rectangular - prism is \(V = l\times w\times h\).
For the two vertical prisms: \(V_1=V_2 = 2\times3\times5=30\) cubic feet.
For the horizontal prism: \(l = 8\), \(w = 2\), \(h = 5\), so \(V_3=8\times2\times5 = 80\) cubic feet.

Step2: Calculate the total volume of the first figure

\(V_{total1}=V_1 + V_2+V_3=30 + 30+80 = 140\) cubic feet.

Step3: Decompose the second figure

The second figure can be decomposed into three rectangular - prisms. Each prism has dimensions \(5\times5\times5\), \(5\times5\times(10 - 5)\) and \(2\times5\times10\).
For the first prism: \(V_4 = 5\times5\times5=125\) cubic inches.
For the second prism: \(V_5=5\times5\times5 = 125\) cubic inches.
For the third prism: \(V_6=2\times5\times10 = 100\) cubic inches.

Step4: Calculate the total volume of the second figure

\(V_{total2}=V_4 + V_5+V_6=125+125 + 100=350\) cubic inches.

Answer:

The volume of the first figure is 140 cubic feet and the volume of the second figure is 350 cubic inches.