### Home > CALC3RD > Chapter Ch9 > Lesson 9.4.1 > Problem9-107

9-107.

The region under $y =\sqrt { x - 1 }$ over the interval $1 ≤ x ≤ a$ for some $a > 1$ is rotated about the line $y = −1$. If the volume of the resulting solid is $10π$ cubic units, what is the value of $a$?

$\int_1^a\Big(\pi(y-(-1))^2-\pi(1)^2\Big)dx=10\pi$