todai-math 2024 Q5

todai-math · Japan · science_official Volumes of Revolution Volume of Revolution about a Horizontal Axis (Evaluate)
In coordinate space, take three points $A(1, 0, 0)$, $B(0, 1, 0)$, $C(0, 0, 1)$, and let $D$ be the midpoint of segment $AC$. Find the volume of the solid obtained by rotating the boundary and interior of triangle $ABD$ one full revolution about the $x$-axis. 
In coordinate space, take three points $A(1, 0, 0)$, $B(0, 1, 0)$, $C(0, 0, 1)$, and let $D$ be the midpoint of segment $AC$. Find the volume of the solid obtained by rotating the boundary and interior of triangle $ABD$ one full revolution about the $x$-axis.
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q6