$\text { Find the volume of the solid generated by rotating the circle } ( x - 10 ) ^ { 2 } + y ^ { 2 } = 16$ about the y-axis.
A) $V = 320 \pi ^ { 2 }$
B) $V = 80 \pi ^ { 2 }$
C) $V = 80 \pi$
D) $V = 320 \pi$
E) $V = 160 \pi ^ { 2 }$

Question

$\text { Find the volume of the solid generated by rotating the circle } ( x - 10 ) ^ { 2 } + y ^ { 2 } = 16$ about the y-axis. 
A) $V = 320 \pi ^ { 2 }$
B) $V = 80 \pi ^ { 2 }$
C) $V = 80 \pi$
D) $V = 320 \pi$
E) $V = 160 \pi ^ { 2 }$

Quizplus · Accepted Answer

The correct answer is A because the volume of the solid generated by rotating the circle about the y-axis is given by the integral of the area of the cross-sections perpendicular to the y-axis. The area of each cross-section is a circle with radius $r = \sqrt { 16 - ( x - 10 ) ^ { 2 } } $, so the volume is:$$V = \int _ { - 4 } ^ { 4 } \pi r ^ { 2 } d x = \int _ { - 4 } ^ { 4 } \pi \left( 16 - ( x - 10 ) ^ { 2 } \right) d x = 320 \pi ^ { 2 }$$

Find the volume of the solid generated by rotating the circle (x−10)2+y2=16\text { Find the volume of the solid generated by rotating the circle } ( x - 10 ) ^ { 2 } + y ^ { 2 } = 16 Find the volume of the solid generated by rotating the circle (x−10)2+y2=16

$\text { Find the volume of the solid generated by rotating the circle } ( x - 10 ) ^ { 2 } + y ^ { 2 } = 16$