Mathematics

Problem

Consider the region bounded by the curves

y=kx

and

y=x^{2}

for

0\le x\le k

, where

k>0

. Squares are erected on this region with bases perpendicular to the

x

–axis; the side of each square equals the vertical distance between the two curves at that

x

–value. If the volume of the resulting solid is

8.1

cubic units, what is the value of

k

? a)

3.6

2.5

3.0

2.4