Question
A cylinder shaped juice pitcher has a diameter of 12 cm and a height of 25 cm.
What volume of juice does the pitcher contain when it is 25% full?
Use 3.14 to approximate pi.
Enter your answer as a decimal to the tenths place in the box.
cma
What volume of juice does the pitcher contain when it is 25% full?
Use 3.14 to approximate pi.
Enter your answer as a decimal to the tenths place in the box.
cma
Answers
GPT-4o mini
To find the volume of juice in a cylindrical pitcher when it is 25% full, we first need to calculate the volume of the entire cylinder. The formula for the volume \( V \) of a cylinder is given by:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.
1. **Calculate the radius**: The diameter of the pitcher is 12 cm, so the radius \( r \) is half of the diameter:
\[
r = \frac{12 \, \text{cm}}{2} = 6 \, \text{cm}
\]
2. **Calculate the volume of the pitcher**:
- Height \( h = 25 \, \text{cm} \)
- Plugging in the values:
\[
V = 3.14 \times (6 \, \text{cm})^2 \times 25 \, \text{cm}
\]
Calculating \( (6 \, \text{cm})^2 \):
\[
(6 \, \text{cm})^2 = 36 \, \text{cm}^2
\]
Now, substitute this back into the volume equation:
\[
V = 3.14 \times 36 \, \text{cm}^2 \times 25 \, \text{cm}
\]
Calculating \( 36 \times 25 \):
\[
36 \times 25 = 900
\]
So, now we have:
\[
V = 3.14 \times 900 \, \text{cm}^3
\]
Calculating this gives:
\[
V = 2826 \, \text{cm}^3
\]
3. **Find the volume when the pitcher is 25% full**:
To find 25% of the total volume:
\[
\text{Volume when 25% full} = 0.25 \times 2826 \, \text{cm}^3
\]
Calculating this:
\[
0.25 \times 2826 = 706.5 \, \text{cm}^3
\]
Thus, the volume of juice when the pitcher is 25% full is:
\[
\boxed{706.5}
\]
So, the final answer, rounded to the tenths place, is **706.5 cm³**.
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.
1. **Calculate the radius**: The diameter of the pitcher is 12 cm, so the radius \( r \) is half of the diameter:
\[
r = \frac{12 \, \text{cm}}{2} = 6 \, \text{cm}
\]
2. **Calculate the volume of the pitcher**:
- Height \( h = 25 \, \text{cm} \)
- Plugging in the values:
\[
V = 3.14 \times (6 \, \text{cm})^2 \times 25 \, \text{cm}
\]
Calculating \( (6 \, \text{cm})^2 \):
\[
(6 \, \text{cm})^2 = 36 \, \text{cm}^2
\]
Now, substitute this back into the volume equation:
\[
V = 3.14 \times 36 \, \text{cm}^2 \times 25 \, \text{cm}
\]
Calculating \( 36 \times 25 \):
\[
36 \times 25 = 900
\]
So, now we have:
\[
V = 3.14 \times 900 \, \text{cm}^3
\]
Calculating this gives:
\[
V = 2826 \, \text{cm}^3
\]
3. **Find the volume when the pitcher is 25% full**:
To find 25% of the total volume:
\[
\text{Volume when 25% full} = 0.25 \times 2826 \, \text{cm}^3
\]
Calculating this:
\[
0.25 \times 2826 = 706.5 \, \text{cm}^3
\]
Thus, the volume of juice when the pitcher is 25% full is:
\[
\boxed{706.5}
\]
So, the final answer, rounded to the tenths place, is **706.5 cm³**.