Question
how many cubic centimeters of water can this paper cone cup hold?
8 cm
9 cm
v cone = 1/3 nr^3 h
answers:
144n
216n
48n
192n
8 cm
9 cm
v cone = 1/3 nr^3 h
answers:
144n
216n
48n
192n
Answers
GPT-4o mini
To find the volume of a cone, the correct formula to use is:
\[
V = \frac{1}{3} \pi r^2 h
\]
Where:
- \(V\) is the volume,
- \(r\) is the radius of the base of the cone,
- \(h\) is the height of the cone.
From your description, it seems like the height of the cone \(h\) is 9 cm. However, you didn't provide the radius \(r\).
Assuming the 8 cm refers to the diameter, the radius \(r\) would be half of that:
\[
r = \frac{8 \, \text{cm}}{2} = 4 \, \text{cm}
\]
Now we can substitute \(r\) and \(h\) into the formula:
\[
V = \frac{1}{3} \pi (4 \, \text{cm})^2 (9 \, \text{cm})
\]
Calculating \(r^2\):
\[
V = \frac{1}{3} \pi (16 \, \text{cm}^2) (9 \, \text{cm})
\]
Now calculate the volume:
\[
V = \frac{1}{3} \pi (144 \, \text{cm}^3)
\]
\[
V = 48 \pi \, \text{cm}^3
\]
If we approximate \(\pi\) as 3.14, we have:
\[
V \approx 48 \times 3.14 \approx 150.72 \, \text{cm}^3
\]
However, in cubic centimeters, the volume of the cone in terms of \(\pi\) is \(48 \pi \, \text{cm}^3\).
Based on your answer choices:
- **144n**
- **216n**
- **48n**
- **192n**
The closest choice, expressed in terms of \(n\), appears to be:
**48n** (if considering \(n = \pi\)), as the final volume is \(48 \pi \, \text{cm}^3\).
\[
V = \frac{1}{3} \pi r^2 h
\]
Where:
- \(V\) is the volume,
- \(r\) is the radius of the base of the cone,
- \(h\) is the height of the cone.
From your description, it seems like the height of the cone \(h\) is 9 cm. However, you didn't provide the radius \(r\).
Assuming the 8 cm refers to the diameter, the radius \(r\) would be half of that:
\[
r = \frac{8 \, \text{cm}}{2} = 4 \, \text{cm}
\]
Now we can substitute \(r\) and \(h\) into the formula:
\[
V = \frac{1}{3} \pi (4 \, \text{cm})^2 (9 \, \text{cm})
\]
Calculating \(r^2\):
\[
V = \frac{1}{3} \pi (16 \, \text{cm}^2) (9 \, \text{cm})
\]
Now calculate the volume:
\[
V = \frac{1}{3} \pi (144 \, \text{cm}^3)
\]
\[
V = 48 \pi \, \text{cm}^3
\]
If we approximate \(\pi\) as 3.14, we have:
\[
V \approx 48 \times 3.14 \approx 150.72 \, \text{cm}^3
\]
However, in cubic centimeters, the volume of the cone in terms of \(\pi\) is \(48 \pi \, \text{cm}^3\).
Based on your answer choices:
- **144n**
- **216n**
- **48n**
- **192n**
The closest choice, expressed in terms of \(n\), appears to be:
**48n** (if considering \(n = \pi\)), as the final volume is \(48 \pi \, \text{cm}^3\).