Consider the right half ( ) of the circle

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider the right half (

x \ge 0

) of the circle

x^{2} + y^{2} = 16

. This semicircular region is the base of a solid whose cross-sections perpendicular to the

y

-axis are squares. Find the exact volume of the solid.