Question

to make a glass sphere, (3,052.08\text{ cm}^3) of molten glass is poured into a mold. using (3.14) for (\pi), eduardo finds the circumference of the sphere using the steps below.

\\v = \frac{4}{3}\pi r^3\\
\\3,052.08 = \frac{4}{3}(3.14)r^3\\
\\729 = r^3\\
\
= 9\text{ cm}\\
\\c = \pi r^2\\
\\c = 254.34\text{ cm}^2\\

which statement about eduardos calculations is true?

• eduardo did not use the correct formula for the circumference.
• eduardo incorrectly used the length of the diameter to find the circumference.
• eduardo incorrectly calculated the radius.
• eduardo did not square the radius correctly in the second formula.

Explanation:

Analyze the volume calculation steps

$$
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The calculation for the radius \(r = 9\text{ cm}\) is correct.

Analyze the circumference calculation steps

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Eduardo used \(C = \pi r^2\), which is the formula for the area of a circle, not the circumference of a circle/sphere.

Identify the correct statement

The statement "Eduardo did not use the correct formula for the circumference" is true because he used the area formula \(A = \pi r^2\) instead of the circumference formula \(C = 2\pi r\).

Answer:

• Eduardo did not use the correct formula for the circumference. (Correct answer)
• Eduardo incorrectly used the length of the diameter to find the circumference.
• Eduardo incorrectly calculated the radius.
• Eduardo did not square the radius correctly in the second formula.