Grades 11-12 Video Solutions 2012-2012_11-12

Video Transcription

Video Summary

The transcript discusses finding the volumes of ellipsoids obtained by rotating an ellipse around the x-axis and y-axis, labeled as \(E_x\) and \(E_y\), respectively. It uses the formula for a sphere's volume, adjusting it to account for the ellipsoid's axes by stretching the sphere's dimensions. Specifically, for \(E_x\), the volume is found by multiplying by \(a^2b\), and for \(E_y\), by \(ab^2\). By comparing these expressions and considering that \(A \textgreater B\), it concludes that the volume of \(E_x\) is greater than that of \(E_y\), leading to the answer: volume of \(E_x\) is greater.

Keywords

ellipsoid

volume

ellipse

rotation

axes