Question

Find the volume of a cylinder whose base is an ellipse with axes of 12 inches and 7 inches. The altitude of the cylinder is 21 inches. Round to the nearest tenth of a cubic inch. A. 1,522.41 in3 B. 1,866.45 in3 C. 1,385.45 in3 D. 1,213.12 in3

Answer 1

if the ellipse has a major axis of 12 inches, that means its major radius is half that, or 6, and if its minor axis is 7, then its minor radius is half that, 3.5.

$\bf \textit{volume of an elliptical cylinder}\\\\ V=\pi ab h~~ \begin{cases} a=\textit{major axis radius}\\ b=\textit{minor axis radius}\\ h=height\\[-0.5em] \hrulefill\\ a=6\\ b=3.5\\ h=21 \end{cases} \\\\\\ V=\pi (6)(3.5)(21)\implies V\approx 1385.44236023309881816203$