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: [ \begin{align*} V&=\frac{2}{3}\pi(27.4)^{3}\ &=\frac{2}{3}\pi(27.4\times27.4\times27.4)\ &=\frac{2}{3}\pi(20403.464)\ &=\frac{40806.928}{3}\pi\ &\approx\frac{40806.928}{3}\times3.14\ &= 13602.30933\times3.14\ &=42711.2513 \end{align*} ]

Step3: Round to the nearest tenth

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

Answer:

(42711.3) cubic inches