Question

fluency and skills practice lesson 3 breaking apart figures to find volume what is the volume of the solid figure? 1 2 3 4 5 6

Explanation:

Step1: Recall volume formula for rectangular - prism

The volume formula for a rectangular - prism is $V = l\times w\times h$, where $l$ is length, $w$ is width, and $h$ is height.

Step2: Solve for problem 1

For the first rectangular - prism with $l = 2$ ft, $w = 2$ ft, and $h = 3$ ft, we substitute into the formula: $V=2\times2\times3= 12$ cubic feet.

Step3: Solve for problem 2

For the second rectangular - prism with $l = 6$ ft, $w = 2$ ft, and $h = 3$ ft, $V = 6\times2\times3=36$ cubic feet.

Step4: Solve for problem 3

We can break this composite figure into two rectangular - prisms. The first has $l = 2$ ft, $w = 2$ ft, $h = 3$ ft, so $V_1=2\times2\times3 = 12$ cubic feet. The second has $l = 4$ ft, $w = 2$ ft, $h = 3$ ft, so $V_2=4\times2\times3=24$ cubic feet. The total volume $V = V_1 + V_2=12 + 24=36$ cubic feet.

Step5: Solve for problem 4

Break the composite figure into two rectangular - prisms. The first has $l = 8$ cm, $w = 2$ cm, $h = 2$ cm, so $V_1=8\times2\times2 = 32$ cubic cm. The second has $l = 2$ cm, $w = 2$ cm, $h = 5$ cm, so $V_2=2\times2\times5 = 20$ cubic cm. The total volume $V=V_1 + V_2=32+20 = 52$ cubic cm.

Step6: Solve for problem 5

Break the composite figure into two rectangular - prisms. The first has $l = 5$ ft, $w = 5$ ft, $h = 2$ ft, so $V_1=5\times5\times2=50$ cubic feet. The second has $l = 6$ ft, $w = 3$ ft, $h = 5 - 2=3$ ft, so $V_2=6\times3\times3 = 18$ cubic feet. The total volume $V=V_1 + V_2=50 + 18=68$ cubic feet.

Step7: Solve for problem 6

Break the composite figure into two rectangular - prisms. The first has $l = 12$ in, $w = 10$ in, $h = 4$ in, so $V_1=12\times10\times4 = 480$ cubic inches. The second has $l = 3$ in, $w = 6$ in, $h = 4$ in, so $V_2=3\times6\times4=72$ cubic inches. The total volume $V=V_1+V_2=480 + 72=552$ cubic inches.

Answer:

1. 12 cubic feet
2. 36 cubic feet
3. 36 cubic feet
4. 52 cubic cm
5. 68 cubic feet
6. 552 cubic inches