Asked by A
Use cylindrical shells to find the volume V of the solid.
A sphere of radius r
A sphere of radius r
Answers
Answered by
Reiny
Let a circle x^2 + y^2 = r^2 be rotated about the x-axis to create the sphere
so we need
volume = π∫ y^2 dx from -r to r or
volume = 2π∫ y^2 dx from 0 to r because of the symmetry
= 2π∫ r^2 - x^2 dx from 0 to r
= 2π [r^2 x - (1/3)x^3 ] from 0 to r
= 2π (r^3 - r^3/3)
= 2π(2/3) r^3
= (4/3)π r^3
so we need
volume = π∫ y^2 dx from -r to r or
volume = 2π∫ y^2 dx from 0 to r because of the symmetry
= 2π∫ r^2 - x^2 dx from 0 to r
= 2π [r^2 x - (1/3)x^3 ] from 0 to r
= 2π (r^3 - r^3/3)
= 2π(2/3) r^3
= (4/3)π r^3
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.