Science:Math Exam Resources/Courses/MATH101 C/April 2024/Question 19/Statement

For a constant $a>0,$ consider the plane region lying above the curve $y=a^{2}x^{2}$ and below the curve $y={\sqrt {ax}}$. Rotating this region around the x-axis produces a solid: let $V_{x}$ denote the resulting volume. Similarly, let $V_{y}$ denote the volume produced by rotating the same region around the $y$-axis.

Find the value of a for which $V_{y}=2V_{x}$.