Question

volume of a sphere (level 1)
score: 4/12 penalty: 1 off
question
what is the volume of a sphere with a radius of 41.8 in, rounded to the nearest tenth of a cubic inch?
answer attempt 2 out of 2
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Explanation:

Step1: Recall the formula for the volume of a sphere

The formula for the volume \( V \) of a sphere with radius \( r \) is \( V=\frac{4}{3}\pi r^{3} \).

Step2: Substitute the given radius into the formula

Given \( r = 41.8 \) inches. Substitute \( r \) into the formula:
\( V=\frac{4}{3}\pi(41.8)^{3} \)
First, calculate \( (41.8)^{3} \):
\( 41.8\times41.8 = 1747.24 \), then \( 1747.24\times41.8=1747.24\times(40 + 1.8)=1747.24\times40+1747.24\times1.8 = 69889.6+3145.032 = 73034.632 \)

Step3: Multiply by \( \frac{4}{3}\pi \)

Now, \( V=\frac{4}{3}\pi\times73034.632 \)
\( \frac{4}{3}\times73034.632=\frac{292138.528}{3}\approx97379.5093 \)
Then, multiply by \( \pi \) (using \( \pi\approx3.14159 \)):
\( V\approx97379.5093\times3.14159\approx305907.4 \) (rounded to the nearest tenth)

Answer:

\( 305907.4 \)