Question

breaking apart figures to find volume
what is the volume of the solid figure?
1
2 ft 2 ft 3 ft
2
6 ft 2 ft 3 ft
3
2 ft 2 ft 4 ft 2 ft 3 ft
4
2 cm 5 cm 7 cm 8 cm
5
2 ft 5 ft 5 ft 6 ft 3 ft
6
12 in. 10 in. 3 in.

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 have $V_1=2\times2\times3= 12$ cubic feet.

Step3: Solve for problem 2

For the second rectangular - prism with $l = 6$ ft, $w = 2$ ft, and $h = 3$ ft, we have $V_2=6\times2\times3 = 36$ cubic feet.

Step4: Solve for problem 3

We can break the L - shaped figure into two rectangular - prisms. One has dimensions $l_1 = 2$ ft, $w_1 = 2$ ft, $h_1 = 3$ ft and the other has $l_2 = 4$ ft, $w_2 = 2$ ft, $h_2 = 3$ ft.
$V_{31}=2\times2\times3 = 12$ cubic feet and $V_{32}=4\times2\times3=24$ cubic feet. Then $V_3=V_{31}+V_{32}=12 + 24=36$ cubic feet.

Step5: Solve for problem 4

Break the L - shaped figure into two rectangular - prisms. One has dimensions $l_1 = 2$ cm, $w_1 = 5$ cm, $h_1 = 2$ cm and the other has $l_2 = 8$ cm, $w_2 = 2$ cm, $h_2 = 2$ cm.
$V_{41}=2\times5\times2 = 20$ cubic cm and $V_{42}=8\times2\times2=32$ cubic cm. Then $V_4=V_{41}+V_{42}=20 + 32 = 52$ cubic cm.

Step6: Solve for problem 5

Break the figure into two rectangular - prisms. One has dimensions $l_1 = 5$ ft, $w_1 = 2$ ft, $h_1 = 5$ ft and the other has $l_2 = 6$ ft, $w_2 = 3$ ft, $h_2 = 2$ ft.
$V_{51}=5\times2\times5=50$ cubic feet and $V_{52}=6\times3\times2 = 36$ cubic feet. Then $V_5=V_{51}+V_{52}=50+36 = 86$ cubic feet.

Step7: Solve for problem 6

Break the figure into two rectangular - prisms. One has dimensions $l_1 = 12$ in, $w_1 = 10$ in, $h_1 = 4$ in and the other has $l_2 = 3$ in, $w_2 = 4$ in, $h_2 = 6$ in.
$V_{61}=12\times10\times4=480$ cubic inches and $V_{62}=3\times4\times6 = 72$ cubic inches. Then $V_6=V_{61}+V_{62}=480+72=552$ cubic inches.

Answer:

Problem 1: 12 cubic feet
Problem 2: 36 cubic feet
Problem 3: 36 cubic feet
Problem 4: 52 cubic cm
Problem 5: 86 cubic feet
Problem 6: 552 cubic inches