Question

what is the volume of a hemisphere with a diameter of 54.8 in, rounded to the nearest tenth of a cubic inch?

Explanation:

Step1: Find the radius

The radius \(r\) of a sphere is half of the diameter. Given \(d = 54.8\) in, so \(r=\frac{d}{2}=\frac{54.8}{2}=27.4\) in.

Step2: Use the formula for the volume of a hemisphere

The formula for the volume \(V\) of a hemisphere is \(V=\frac{2}{3}\pi r^{3}\).
Substitute \(r = 27.4\) into the formula:

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Step3: Round to the nearest tenth

Rounding \(42711.2513\) to the nearest tenth gives \(42711.3\).

Answer:

\(42711.3\) cubic inches