Question
If the volume of a spherical ball is 1437 cubic inches, what is the radius? Step 1: V= 4/3 π r^3 Substitute in 1437 for V and solve for r. Step 2: frac 148T= 4/3 r^3 Divide byπ on both sides Step 3: f(3))/3r =r^3 Multiply by 4 and Divide by 3 on both sides Step 4: 4[143T]/33π =r ==> Divide by 3 on both sides There are 2 mistakes in this process. Choose the correct 2 mistakes. (2 points) Step 1 used the wrong formula for a sphere Step 2 should have multiplied by π 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 Seep 4 should have taken the square root instead of dividing by 3
Answers
GPT-4o mini
Let's look at the steps you've provided with the corresponding formula for the volume of a sphere:
**Step 1: V = (4/3)πr³**
This step is correct, as you have used the appropriate formula for the volume of a sphere.
**Step 2: Substitute in 1437 for V and solve for r.**
Here you're supposed to set up the equation correctly:
1437 = (4/3)πr³
You can then divide both sides by π, which has been correctly stated, but the form used in the given process is confusing.
**Step 3: Multiply by 4 and Divide by 3 on both sides**
This step is where the first mistake occurs. You should multiply both sides by (3/4) (rather than "4 and divide by 3") after dividing by π.
**Step 4: Divide by 3 on both sides**
This is also incorrect, as after getting (3 * 1437)/(4π) = r³, you need to take the cube root to find r.
To summarize, the two mistakes in this process are:
1. **Step 3 should have multiplied by 3 and divided by 4 on both sides.**
2. **Step 4 should have taken the cube root instead of dividing by 3.**
So your final answer regarding the two mistakes is:
- 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 1: V = (4/3)πr³**
This step is correct, as you have used the appropriate formula for the volume of a sphere.
**Step 2: Substitute in 1437 for V and solve for r.**
Here you're supposed to set up the equation correctly:
1437 = (4/3)πr³
You can then divide both sides by π, which has been correctly stated, but the form used in the given process is confusing.
**Step 3: Multiply by 4 and Divide by 3 on both sides**
This step is where the first mistake occurs. You should multiply both sides by (3/4) (rather than "4 and divide by 3") after dividing by π.
**Step 4: Divide by 3 on both sides**
This is also incorrect, as after getting (3 * 1437)/(4π) = r³, you need to take the cube root to find r.
To summarize, the two mistakes in this process are:
1. **Step 3 should have multiplied by 3 and divided by 4 on both sides.**
2. **Step 4 should have taken the cube root instead of dividing by 3.**
So your final answer regarding the two mistakes is:
- 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.