MathDB

Let

k

and

a

are positive constants. Denote by

V_1

the volume of the solid generated by a rotation of the figure enclosed by the curve

C: y=\frac{x}{x+k}\ (x\geq 0)

, the line

x=a

and the

x

-axis around the

x

-axis, and denote by

V_2

that of the solid by a rotation of the figure enclosed by the curve

C

, the line

y=\frac{a}{a+k}

and the

y

-axis around the

y

-axis. Find the ratio

\frac{V_2}{V_1}.

Problem Statement