The volume of the solid obtained by rotating the plane region enclosed by $y = x ^ { 4 } , y = 1 , \text { and } x = 0$ about the x = 1 is
A) $\frac { 7 \pi } { 15 }$
B) $\frac { 2 \pi } { 3 }$
C) $\frac { 14 \pi } { 15 }$
D) $\frac { 14 } { 15 }$
E) $\frac { 14 \pi } { 3 }$
F) $\frac { 7 \pi } { 5 }$
G) $\frac { 14 \pi } { 5 }$
H) $\frac { 7 } { 15 }$

Question

The volume of the solid obtained by rotating the plane region enclosed by $y = x ^ { 4 } , y = 1 , \text { and } x = 0$ about the x = 1 is
A) $\frac { 7 \pi } { 15 }$ 
B) $\frac { 2 \pi } { 3 }$ 
C) $\frac { 14 \pi } { 15 }$ 
D) $\frac { 14 } { 15 }$ 
E) $\frac { 14 \pi } { 3 }$ 
F) $\frac { 7 \pi } { 5 }$ 
G) $\frac { 14 \pi } { 5 }$ 
H) $\frac { 7 } { 15 }$

Quizplus · Accepted Answer

The correct answer is C because the volume of the solid obtained by rotating the plane region enclosed by $y = x ^ { 4 } , y = 1 , \text { and } x = 0$ about the x = 1 is $\frac { 14 \pi } { 15 }$.

The Volume of the Solid Obtained by Rotating the Plane y=x4,y=1, and x=0y = x ^ { 4 } , y = 1 , \text { and } x = 0y=x4,y=1, and x=0

The Volume of the Solid Obtained by Rotating the Plane $y = x ^ { 4 } , y = 1 , \text { and } x = 0$