Question
If the volume of a spherical ball is 1437 cubic inches, what is the radius?
Step 1: V=43πr3
---> Substitute in 1437 for V and solve for r.
Step 2: 1437π=43r3
---> Divide by π
on both sides
Step 3: 4(1437)3π=r3
---> Multiply by 4 and Divide by 3 on both sides
Step 4: 4(1437)3⋅3π=r
---> Divide by 3 on both sides
There are 2 mistakes in this process. Choose the correct 2 mistakes.
(2 points)
Responses
Step 1 used the wrong formula for a sphere
Step 1 used the wrong formula for a sphere
Step 2 should have multiplied by π
on both sides
Step 2 should have multiplied by pi on both sides
Step 3 should have multiplied by 3 and divided by 4 on both sides
Step 3 should have multiplied by 3 and divided by 4 on both sides
Step 4 should have taken the cube root instead of dividing by 3
Step 4 should have taken the cube root instead of dividing by 3
Step 4 should have taken the square root instead of dividing by 3
Step 4 should have taken the square root instead of dividing by 3
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Step 1: V=43πr3
---> Substitute in 1437 for V and solve for r.
Step 2: 1437π=43r3
---> Divide by π
on both sides
Step 3: 4(1437)3π=r3
---> Multiply by 4 and Divide by 3 on both sides
Step 4: 4(1437)3⋅3π=r
---> Divide by 3 on both sides
There are 2 mistakes in this process. Choose the correct 2 mistakes.
(2 points)
Responses
Step 1 used the wrong formula for a sphere
Step 1 used the wrong formula for a sphere
Step 2 should have multiplied by π
on both sides
Step 2 should have multiplied by pi on both sides
Step 3 should have multiplied by 3 and divided by 4 on both sides
Step 3 should have multiplied by 3 and divided by 4 on both sides
Step 4 should have taken the cube root instead of dividing by 3
Step 4 should have taken the cube root instead of dividing by 3
Step 4 should have taken the square root instead of dividing by 3
Step 4 should have taken the square root instead of dividing by 3
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Answers
GPT-4o mini
The two mistakes in the process are:
1. **Step 1 used the wrong formula for a sphere.** The correct formula for the volume \( V \) of a sphere is given by \( V = \frac{4}{3} \pi r^3 \). This part of the process was correct, so Option 1 is not a mistake.
2. **Step 4 should have taken the cube root instead of dividing by 3.** Once you isolate \( r^3 \), to solve for \( r \), you would need to take the cube root of both sides, rather than dividing by 3.
So the correct answers for the mistakes are:
- Step 1 used the wrong formula for a sphere (this is actually correct as per original context).
- Step 4 should have taken the cube root instead of dividing by 3 (this is correct).
The correct identification of mistakes should be based on the reasoning provided—though only one of the stated errors really exists in terms of the mathematics shown.
1. **Step 1 used the wrong formula for a sphere.** The correct formula for the volume \( V \) of a sphere is given by \( V = \frac{4}{3} \pi r^3 \). This part of the process was correct, so Option 1 is not a mistake.
2. **Step 4 should have taken the cube root instead of dividing by 3.** Once you isolate \( r^3 \), to solve for \( r \), you would need to take the cube root of both sides, rather than dividing by 3.
So the correct answers for the mistakes are:
- Step 1 used the wrong formula for a sphere (this is actually correct as per original context).
- Step 4 should have taken the cube root instead of dividing by 3 (this is correct).
The correct identification of mistakes should be based on the reasoning provided—though only one of the stated errors really exists in terms of the mathematics shown.