### Home > CALC > Chapter 8 > Lesson 8.3.2 > Problem8-110

8-110.

Uh-oh! Arlen needs your help. He is trying to write an integral for the volume of square cross-sections perpendicular to the $y$-axis where the base is the region bounded by the $y$-axis and $y = x^2$ on the interval $0 ≤ x ≤ 3$. Help him set up this integral.

These cross sections are squares. Their area formula is well known.

The function and the bounds must be in terms of $y$, because the cross sections are perpendicular to the $y$-axis. So, rewrite the function in terms of $y$ and find the $y$-values that correspond with the given domain.