Let . Region is bounded by , , and . When is revolved about the horizontal line , the…

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

k>4

. Region

S

is bounded by

y=x

y=0

, and

x=4

. When

S

is revolved about the horizontal line

y=k

, the volume

V(k)

of the resulting solid is best expressed by which of the following? (a)

V(k)=\pi\displaystyle\int_{0}^{4}\bigl[k^{2}-x^{2}\bigr]dx

(b)

V(k)=\pi\displaystyle\int_{0}^{4}\bigl[k^{2}-(k-x)\bigr]dx

(c)

V(k)=\pi\displaystyle\int_{0}^{k}\bigl[k^{2}-(k-x)^{2}\bigr]dx

(d)

V(k)=\pi\displaystyle\int_{0}^{4}\bigl[k^{2}-(k-x)^{2}\bigr]dx