Mathematics

Problem

The base of a solid is the region between the lines

y=kx

and

y=0

from

x=0

x=5

. At each

x

, the cross section perpendicular to the

x

–axis is a semicircle whose diameter equals the distance between the two lines at that

x

. If the volume of the solid is

100\pi

cubic units, determine the value of

k\,(k>0)