Mth 163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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This is a problem that I do not understand. Although I can see how you solved the formula, I don't understand why. Why is my solution not correct? Using a calculator, I multiplied (4/3)*64 *pi, with 64 being the result of 4^3. This is somewhat similar to the question I sent about a previous problem, where I understand the problem and the formula, I just don't understand why it is calculated the way it is.
Self-critique Rating:
Question: `q008. What is a volume of a sphere whose radius is 4 meters?
Your solution: V=(4/3)*pi*4^3, V=(4/3)*pi*64, V=85.3*pi, V=267.9
Confidence Assessment: 2
Given Solution:
`aThe volume of a sphere is V = 4/3 pi r^3, where r is the radius of the sphere. In this case r = 4 m so
V = 4/3 pi * (4 m)^3 = 4/3 pi * 4^3 m^3 = 256/3 pi m^3.
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4/3 * 64 = 4/3 * 64/1 = 4 * 64 / (3 * 1) = 256 / 3. So 4/3 * 64 * pi = 256 / 3 * pi, which by order of operations is (256 / 3) * pi.
This can also be written 256 pi / 3.
This result is exact, so if the exact radius is 4, the exact volume is 256 pi / 3.
Your result, 267.9, is nearly equal to the exact result, but is not quite the same.
If there is uncertainty in the radius 4, then an approximation to the appropriate number of significant figures is as good as the exact expression given above. If the radius is exact, then only the exact expression is entirely correct.