Question

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

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, $V_1=2\times2\times3= 12$ ft³.

Step3: Solve for problem 2

For the second rectangular - prism with $l = 6$ ft, $w = 2$ ft and $h = 3$ ft, $V_2=6\times2\times3 = 36$ ft³.

Step4: Solve for problem 3

Break the figure into two rectangular - prisms.
First prism: $l = 2$ ft, $w = 2$ ft, $h = 3$ ft, $V_{31}=2\times2\times3 = 12$ ft³.
Second prism: $l = 4$ ft, $w = 2$ ft, $h = 3$ ft, $V_{32}=4\times2\times3=24$ ft³.
Total volume $V_3=V_{31}+V_{32}=12 + 24=36$ ft³.

Step5: Solve for problem 4

Break the L - shaped figure into two rectangular - prisms.
First prism: $l = 8$ cm, $w = 2$ cm, $h = 2$ cm, $V_{41}=8\times2\times2=32$ cm³.
Second prism: $l = 2$ cm, $w = 2$ cm, $h=(7 - 2)=5$ cm, $V_{42}=2\times2\times5 = 20$ cm³.
Total volume $V_4=V_{41}+V_{42}=32+20 = 52$ cm³.

Answer:

1. $12$ ft³
2. $36$ ft³
3. $36$ ft³
4. $52$ cm³