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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

1 answer

Let's analyze the steps and identify the mistakes:

  1. Step 1: The formula for the volume of a sphere is \( V = \frac{4}{3}\pi r^3 \). The equation used in Step 1 (V=43πr3) is incorrect because it lacks the fraction. So, the first mistake is indeed that this step used the wrong formula for a sphere.

  2. Step 2: The transition from \( 1437 = \frac{4}{3} r^3 \) to \( 1437\pi = \frac{4}{3}r^3 \) is incorrect. This step should have kept the equation correct with respect to division by π. This means that the mistake in this step would be better phrased as failing to recognize how to isolate terms properly.

  3. Step 3: This step appears to miss the correct application of algebra. The transition should be focused on isolating \( r^3 \) rather than multiplying terms erroneously. The adjustment needs to simply focus on \( r^3 \), not arbitrary multiplication.

  4. Step 4: Here, the error is in claiming to divide by 3 instead of taking the cube root of \( r^3 \).

Based on this analysis, the mistakes are:

  1. Step 1 used the wrong formula for a sphere.
  2. Step 4 should have taken the cube root instead of dividing by 3.

So, the correct responses are:

  • Step 1 used the wrong formula for a sphere.
  • Step 4 should have taken the cube root instead of dividing by 3.