Mathematics

Problem

Consider the region bounded by the curve

y=\sin x

and the

x

–axis on

0\le x\le \pi

. At each

x

, a cross section taken perpendicular to the

x

–axis is an isosceles right triangle whose legs lie in the base and have length

k\sin x

. If the volume of the resulting solid is

\dfrac{25\pi}{4}

cubic units, find the value of the constant

k\,(k>0)