Question

volume of a sphere (level 1)
score: 4/9 penalty: 1 off
question
what is the volume of a sphere with a diameter of 7.9 ft, rounded to the nearest tenth of a cubic foot?

Explanation:

Step1: Calculate the radius

The radius \(r\) of a sphere is half of the diameter \(d\). Given \(d = 7.9\) ft, then \(r=\frac{d}{2}=\frac{7.9}{2}=3.95\) ft.

Step2: Use the volume formula for a sphere

The volume formula of a sphere is \(V=\frac{4}{3}\pi r^{3}\). Substitute \(r = 3.95\) into the formula:

$$
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Step3: Round to the nearest tenth

Rounding \(258.023743\cdots\) to the nearest tenth. The digit in the hundredth place is \(2\), so we keep the tenths place digit as it is.

Answer:

\(258.0\) cubic feet