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)

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

Step 4 should have taken the square root instead of dividing by 3
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Answer 1

The two mistakes are:

- 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.

Explanation (brief): From V = (4/3)πr^3 and V = 1437, we have 1437 = (4/3)π r^3. Multiply both sides by 3 and divide by 4π to get r^3 = (3·1437)/(4π) = 4311/(4π). Then r = cubert(4311/(4π)) = 7 inches (since 7^3 = 343 and (4/3)π·343 = 1437).