Question
When calculating the volume of this ball, Phil used the volume formula V = pi * r ^ 2 * h
Here is his work:
V = pi ● r² ● h
= (3.14) ● (5²) ● (10)
= (3.14) ● (25) ● (10)
= 785 N³
Did Phil find the correct volume for the ball?
If yes, explain what is happening in each step of his work.
If no, identify his mistake and find the correct volume. Make sure to show your steps and calculations.
Make sure no one can find this
Make it look like a 8th grader wrote it
Here is his work:
V = pi ● r² ● h
= (3.14) ● (5²) ● (10)
= (3.14) ● (25) ● (10)
= 785 N³
Did Phil find the correct volume for the ball?
If yes, explain what is happening in each step of his work.
If no, identify his mistake and find the correct volume. Make sure to show your steps and calculations.
Make sure no one can find this
Make it look like a 8th grader wrote it
Answers
Answered by
GPT-4o mini
No, Phil did not find the correct volume for the ball. He made a mistake in using the formula. The formula he used, \( V = \pi \times r^2 \times h \), is actually for the volume of a cylinder, not a sphere (ball).
The correct formula for the volume of a sphere is:
\[
V = \frac{4}{3} \pi r^3
\]
Let’s calculate the volume of the ball using the correct formula, with \( r = 5 \) (the radius).
1. **Find \( r^3 \)**:
\[
r^3 = 5^3 = 5 \times 5 \times 5 = 125
\]
2. **Plug into the sphere volume formula**:
\[
V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi \times 125
\]
3. **Calculate \( \frac{4}{3} \times 125 \)**:
\[
\frac{4 \times 125}{3} = \frac{500}{3} \approx 166.67
\]
4. **Now multiply by \( \pi \)** (approximating \( \pi \) as 3.14):
\[
V \approx 166.67 \times 3.14 \approx 523.33
\]
So the volume of the ball is approximately \( 523.33 \, N^3 \).
In summary, Phil used the wrong formula for a sphere and calculated the volume of a cylinder instead. The correct volume of the sphere is about \( 523.33 \, N^3 \).
The correct formula for the volume of a sphere is:
\[
V = \frac{4}{3} \pi r^3
\]
Let’s calculate the volume of the ball using the correct formula, with \( r = 5 \) (the radius).
1. **Find \( r^3 \)**:
\[
r^3 = 5^3 = 5 \times 5 \times 5 = 125
\]
2. **Plug into the sphere volume formula**:
\[
V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi \times 125
\]
3. **Calculate \( \frac{4}{3} \times 125 \)**:
\[
\frac{4 \times 125}{3} = \frac{500}{3} \approx 166.67
\]
4. **Now multiply by \( \pi \)** (approximating \( \pi \) as 3.14):
\[
V \approx 166.67 \times 3.14 \approx 523.33
\]
So the volume of the ball is approximately \( 523.33 \, N^3 \).
In summary, Phil used the wrong formula for a sphere and calculated the volume of a cylinder instead. The correct volume of the sphere is about \( 523.33 \, N^3 \).