Question
A mug has a diameter of 9 centimeters and a height of 11 centimeters.
Which of the following is the closest to the volume of the mug?
Which of the following is the closest to the volume of the mug?
Answers
GPT-4o mini
To find the volume of the mug, which can be modeled as a cylinder, we use the formula for the volume of a cylinder:
\[
V = \pi r^2 h
\]
Where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
1. **Calculate the radius**: The diameter of the mug is 9 centimeters, so the radius \( r \) is half of that:
\[
r = \frac{9}{2} = 4.5 \text{ cm}
\]
2. **Height of the mug**: The height \( h \) of the mug is given as 11 centimeters.
3. **Calculate the volume**:
\[
V = \pi (4.5)^2 (11)
\]
First, calculate \( (4.5)^2 \):
\[
(4.5)^2 = 20.25
\]
Now substitute this back into the volume formula:
\[
V = \pi (20.25)(11)
\]
Continue the calculation:
\[
V = \pi (222.75)
\]
So the volume is approximately:
\[
V \approx 3.14 \times 222.75 \approx 700.43 \text{ cm}^3
\]
Thus, the closest value to the volume of the mug is approximately \(\mathbf{700.43 \, \text{cm}^3}\).
\[
V = \pi r^2 h
\]
Where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
1. **Calculate the radius**: The diameter of the mug is 9 centimeters, so the radius \( r \) is half of that:
\[
r = \frac{9}{2} = 4.5 \text{ cm}
\]
2. **Height of the mug**: The height \( h \) of the mug is given as 11 centimeters.
3. **Calculate the volume**:
\[
V = \pi (4.5)^2 (11)
\]
First, calculate \( (4.5)^2 \):
\[
(4.5)^2 = 20.25
\]
Now substitute this back into the volume formula:
\[
V = \pi (20.25)(11)
\]
Continue the calculation:
\[
V = \pi (222.75)
\]
So the volume is approximately:
\[
V \approx 3.14 \times 222.75 \approx 700.43 \text{ cm}^3
\]
Thus, the closest value to the volume of the mug is approximately \(\mathbf{700.43 \, \text{cm}^3}\).