MathDB

Given a solid

R

contained in a semi cylinder with the hight

1

which has a semicircle with radius

1

as the base. The cross section at the hight

x\ (0\leq x\leq 1)

is the form combined with two right-angled triangles as attached figure as below. Answer the following questions.
(1) Find the cross-sectional area

S(x)

at the hight

x

.
(2) Find the volume of

R

. If necessary, when you integrate, set

x=\sin t.

Problem Statement