Question
Determine the volume of the figure. Use
3.14
3.14 for
π
π.
The Singh family buys a new dining room table made of solid wood. What is the volume of the Singh family’s new table? Round to the nearest hundredth.
A composite shape in the shape of a table with one central post. The composite shape is composed of a base that is a cylinder and a top that is a rectangular prism. The cylinder has a diameter of 2 feet and a height of 3 feet. The rectangular prism has a length of 9 feet, a width of 4 feet, and a height of 1 foot.
ft
3
3
Answers
Answered by
GPT-4o mini
To calculate the total volume of the dining room table made of solid wood, we need to find the volumes of both the cylindrical base and the rectangular prism top, and then add them together.
**Step 1: Volume of the cylinder (the base)**
The formula for the volume of a cylinder is:
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height.
Given:
- Diameter of the cylinder = 2 feet, so radius \( r = \frac{2}{2} = 1 \) foot.
- Height of the cylinder \( h = 3 \) feet.
Now, substituting the values into the formula:
\[
V = 3.14 \times (1)^2 \times 3 = 3.14 \times 1 \times 3 = 9.42 \text{ cubic feet}
\]
**Step 2: Volume of the rectangular prism (the top)**
The formula for the volume of a rectangular prism is:
\[
V = l \times w \times h
\]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
Given:
- Length \( l = 9 \) feet
- Width \( w = 4 \) feet
- Height \( h = 1 \) foot
Now, substituting the values into the formula:
\[
V = 9 \times 4 \times 1 = 36 \text{ cubic feet}
\]
**Step 3: Total volume of the table**
Now we can find the total volume by adding the volume of the cylinder and the volume of the rectangular prism:
\[
\text{Total Volume} = \text{Volume of Cylinder} + \text{Volume of Rectangular Prism}
\]
\[
\text{Total Volume} = 9.42 + 36 = 45.42 \text{ cubic feet}
\]
Thus, the total volume of the Singh family’s new dining room table is \( \boxed{45.42} \) cubic feet.
**Step 1: Volume of the cylinder (the base)**
The formula for the volume of a cylinder is:
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height.
Given:
- Diameter of the cylinder = 2 feet, so radius \( r = \frac{2}{2} = 1 \) foot.
- Height of the cylinder \( h = 3 \) feet.
Now, substituting the values into the formula:
\[
V = 3.14 \times (1)^2 \times 3 = 3.14 \times 1 \times 3 = 9.42 \text{ cubic feet}
\]
**Step 2: Volume of the rectangular prism (the top)**
The formula for the volume of a rectangular prism is:
\[
V = l \times w \times h
\]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
Given:
- Length \( l = 9 \) feet
- Width \( w = 4 \) feet
- Height \( h = 1 \) foot
Now, substituting the values into the formula:
\[
V = 9 \times 4 \times 1 = 36 \text{ cubic feet}
\]
**Step 3: Total volume of the table**
Now we can find the total volume by adding the volume of the cylinder and the volume of the rectangular prism:
\[
\text{Total Volume} = \text{Volume of Cylinder} + \text{Volume of Rectangular Prism}
\]
\[
\text{Total Volume} = 9.42 + 36 = 45.42 \text{ cubic feet}
\]
Thus, the total volume of the Singh family’s new dining room table is \( \boxed{45.42} \) cubic feet.