Question

breaking apart figures to find volume
what is the volume of the solid figure?
v = l×w×h

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 the length, $w$ is the width, and $h$ is the height.

Step2: Analyze the first figure (top - left)

For the first rectangular - prism with $l = 2$ ft, $w = 2$ ft, and $h = 3$ ft, using the formula $V_1=2\times2\times3 = 12$ cubic feet.

Step3: Analyze the second figure (top - right)

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

Step4: Analyze the third figure (middle - left)

We can break this L - shaped figure into two rectangular - prisms. One has $l = 2$ ft, $w = 2$ ft, $h = 3$ ft and the other has $l = 4$ ft, $w = 2$ ft, $h = 3$ ft.
$V_{31}=2\times2\times3 = 12$ cubic feet and $V_{32}=4\times2\times3 = 24$ cubic feet. The total volume $V_3=V_{31}+V_{32}=12 + 24=36$ cubic feet.

Step5: Analyze the fourth figure (middle - right)

Break the L - shaped figure into two rectangular - prisms. One has $l = 8$ cm, $w = 2$ cm, $h = 2$ cm and the other has $l = 2$ cm, $w = 2$ cm, $h = 5$ cm.
$V_{41}=8\times2\times2=32$ cubic cm and $V_{42}=2\times2\times5 = 20$ cubic cm. The total volume $V_4=V_{41}+V_{42}=32+20 = 52$ cubic cm.

Step6: Analyze the fifth figure (bottom - left)

Assume it is a rectangular - prism with $l = 6$ ft, $w = 3$ ft (height not fully clear from the image, assume a height to calculate). If we assume a height of 1 ft (since not given otherwise), $V_5=6\times3\times1 = 18$ cubic feet.

Step7: Analyze the sixth figure (bottom - right)

Break the L - shaped figure into two rectangular - prisms. One has $l = 10$ in, $w = 4$ in, $h = 6$ in and the other has $l = 4$ in, $w = 3$ in, $h = 6$ in.
$V_{61}=10\times4\times6=240$ cubic inches and $V_{62}=4\times3\times6 = 72$ cubic inches. The total volume $V_6=V_{61}+V_{62}=240+72=312$ cubic inches.

Since the question asks for the volume of the solid figure in general without specifying which one, if we consider the first figure (top - left) as the reference:

Answer:

12 cubic feet