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 3 2 ft 2 ft 4 ft 3 ft 4 5 cm 2 cm 8

Explanation:

1. For the first rectangular - prism (figure 1):

• # Explanation:
• ## Step1: Recall the volume formula for a 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: Identify the dimensions

Here, \(l = 2\) ft, \(w = 2\) ft, and \(h = 3\) ft.

• ## Step3: Calculate the volume

\(V=2\times2\times3= 12\) cubic feet.

• # Answer: \(12\) cubic feet

1. For the second rectangular - prism (figure 2):

• # Explanation:
• ## Step1: Recall the volume formula

The volume formula for a rectangular - prism is \(V = l\times w\times h\).

• ## Step2: Identify the dimensions

Assume the width \(w = 2\) ft and height \(h = 3\) ft (not shown in the figure but we can assume the same cross - sectional dimensions as in the previous problem for a similar - looking rectangular - prism), and \(l = 6\) ft.

• ## Step3: Calculate the volume

\(V = 2\times3\times6=36\) cubic feet.

• # Answer: \(36\) cubic feet

1. For the third composite figure (figure 3):

• # Explanation:
• ## Step1: Split the figure into two rectangular - prisms

We can split the figure into a \(2\times2\times3\) rectangular - prism and a \(4\times2\times3\) rectangular - prism.

• ## Step2: Calculate the volume of the first sub - prism

For the \(2\times2\times3\) rectangular - prism, \(V_1=2\times2\times3 = 12\) cubic feet.

• ## Step3: Calculate the volume of the second sub - prism

For the \(4\times2\times3\) rectangular - prism, \(V_2=4\times2\times3=24\) cubic feet.

• ## Step4: Calculate the total volume

\(V = V_1 + V_2=12 + 24=36\) cubic feet.

• # Answer: \(36\) cubic feet

1. (Since the fourth figure is cut off and no complete dimensions are visible, we cannot solve it with the given information).

Answer:

1. For the first rectangular - prism (figure 1):

• # Explanation:
• ## Step1: Recall the volume formula for a 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: Identify the dimensions

Here, \(l = 2\) ft, \(w = 2\) ft, and \(h = 3\) ft.

• ## Step3: Calculate the volume

\(V=2\times2\times3= 12\) cubic feet.

• # Answer: \(12\) cubic feet

1. For the second rectangular - prism (figure 2):

• # Explanation:
• ## Step1: Recall the volume formula

The volume formula for a rectangular - prism is \(V = l\times w\times h\).

• ## Step2: Identify the dimensions

Assume the width \(w = 2\) ft and height \(h = 3\) ft (not shown in the figure but we can assume the same cross - sectional dimensions as in the previous problem for a similar - looking rectangular - prism), and \(l = 6\) ft.

• ## Step3: Calculate the volume

\(V = 2\times3\times6=36\) cubic feet.

• # Answer: \(36\) cubic feet

1. For the third composite figure (figure 3):

• # Explanation:
• ## Step1: Split the figure into two rectangular - prisms

We can split the figure into a \(2\times2\times3\) rectangular - prism and a \(4\times2\times3\) rectangular - prism.

• ## Step2: Calculate the volume of the first sub - prism

For the \(2\times2\times3\) rectangular - prism, \(V_1=2\times2\times3 = 12\) cubic feet.

• ## Step3: Calculate the volume of the second sub - prism

For the \(4\times2\times3\) rectangular - prism, \(V_2=4\times2\times3=24\) cubic feet.

• ## Step4: Calculate the total volume

\(V = V_1 + V_2=12 + 24=36\) cubic feet.

• # Answer: \(36\) cubic feet

1. (Since the fourth figure is cut off and no complete dimensions are visible, we cannot solve it with the given information).