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 3 ft 4 ft 2 ft 4. 2 cm 5 cm 8 cm 2 cm 5. 5 ft 5 ft 2 ft 6 ft 3 ft 6. 12 in. 10 in.

Question

Accepted Answer

1. **For figure 1**:
   - # 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: Identify dimensions
       Here, $l = 2$ ft, $w = 2$ ft, $h = 3$ ft.
     - ## Step3: Calculate volume
       $V=2\times2\times3= 12$ cubic feet.
   - # Answer:
     $12$ cubic feet
2. **For figure 2**:
   - # Explanation:
     - ## Step1: Use volume formula for rectangular - prism
       $V = l\times w\times h$.
     - ## Step2: Identify dimensions
       $l = 6$ ft, $w = 2$ ft, $h = 3$ ft.
     - ## Step3: Calculate volume
       $V = 6\times2\times3=36$ cubic feet.
   - # Answer:
     $36$ cubic feet
3. **For figure 3**:
   - # Explanation:
     - ## Step1: Split the figure into two rectangular - prisms
       One with dimensions $l_1 = 2$ ft, $w_1 = 2$ ft, $h_1 = 3$ ft and another with $l_2 = 4$ ft, $w_2 = 2$ ft, $h_2 = 3$ ft.
     - ## Step2: Calculate volume of first prism
       $V_1=l_1\times w_1\times h_1=2\times2\times3 = 12$ cubic feet.
     - ## Step3: Calculate volume of second prism
       $V_2=l_2\times w_2\times h_2=4\times2\times3 = 24$ cubic feet.
     - ## Step4: Find total volume
       $V = V_1+V_2=12 + 24=36$ cubic feet.
   - # Answer:
     $36$ cubic feet
4. **For figure 4**:
   - # Explanation:
     - ## Step1: Split the figure into two rectangular - prisms
       One with $l_1 = 8$ cm, $w_1 = 2$ cm, $h_1 = 2$ cm and another with $l_2 = 2$ cm, $w_2 = 2$ cm, $h_2 = 5$ cm.
     - ## Step2: Calculate volume of first prism
       $V_1=l_1\times w_1\times h_1=8\times2\times2=32$ cubic cm.
     - ## Step3: Calculate volume of second prism
       $V_2=l_2\times w_2\times h_2=2\times2\times5 = 20$ cubic cm.
     - ## Step4: Find total volume
       $V=V_1 + V_2=32+20 = 52$ cubic cm.
   - # Answer:
     $52$ cubic cm
5. **For figure 5**:
   - # Explanation:
     - ## Step1: Split the figure into two rectangular - prisms
       One with $l_1 = 5$ ft, $w_1 = 5$ ft, $h_1 = 2$ ft and another with $l_2 = 5$ ft, $w_2 = 1$ ft, $h_2 = 3$ ft.
     - ## Step2: Calculate volume of first prism
       $V_1=l_1\times w_1\times h_1=5\times5\times2=50$ cubic feet.
     - ## Step3: Calculate volume of second prism
       $V_2=l_2\times w_2\times h_2=5\times1\times3 = 15$ cubic feet.
     - ## Step4: Find total volume
       $V=V_1+V_2=50 + 15=65$ cubic feet.
   - # Answer:
     $65$ cubic feet
6. **For figure 6**:
   - # Explanation:
     - ## Step1: Use volume formula for rectangular - prism
       $V = l\times w\times h$.
     - ## Step2: Identify dimensions
       $l = 12$ in, $w = 10$ in, $h = 12$ in.
     - ## Step3: Calculate volume
       $V=12\times10\times12 = 1440$ cubic inches.
   - # Answer:
     $1440$ cubic inches

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