Question 705014

Area of semi-circle = $\frac{1}{2}\pi r^2$. Total flow rate = $Area_A \times s + Area_B \times s = Area_C \times V$. Given radii $r_A=3x, r_B=4x, r_C=5x$.

$\frac{1}{2}\pi(3x)^2 s + \frac{1}{2}\pi(4x)^2 s = \frac{1}{2}\pi(5x)^2 V$. $9x^2 s + 16x^2 s = 25x^2 V$. $25x^2 s = 25x^2 V \implies V = s$.