A solid has its base in the -plane and is bounded on the left by and on the right by for

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

Problem

A solid has its base in the

xy

-plane and is bounded on the left by

x=0

and on the right by

x=y^{2}

for

0\le y\le 4

. At each

y

, the cross section perpendicular to the

y

–axis is a semicircle whose diameter equals

m y^{2}

, where

m>0

is a constant. If the volume of the solid is

200\pi

cubic units, determine the value of

m