MathDB

xyz

space, let

A

be the solid generated by a rotation of the figure, enclosed by the curve

y=2-2x^2

and the

x

-axis about the

y

-axis.
(1) When the solid is cut by the plane

x=a\ (|a|\leq 1)

, find the inequality which expresses the figure of the cross-section.
(2) Denote by

L

the distance between the point

(a,\ 0,\ 0)

and the point on the perimeter of the cross-section found in (1), find the maximum value of

L

.
(3) Find the volume of the solid by a rotation of the solid

A

about the

x

-axis.
1987 Sophia University entrance exam/Science and Technology

Problem Statement