A plate occupies the region bounded by and

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

Problem

A plate occupies the region bounded by

x=0

and

x=4-y^{2}

, where all dimensions are measured in inches. Perpendicular to the

y

-axis, cross sections of a solid are semicircles whose diameters lie in the plate. Compute the volume of the solid in cubic centimeters. (Use

1\ \text{inch}=2.54\ \text{cm}