1. Suppose we accept a solid apple of ambit 4 meters with connected body 8 kilograms per cubic meter. A annular aperture of ambit 9/4 meters is accomplished through the apple so that the arbor of the aperture corresponds to a bore of the aboriginal sphere. Call the actual solid Q.

a) Find the aggregate of Q. Warning: the simple geometrical formulas for spheres and cylinders will not accord the actual answer. You will charge to use an integral.

I accept to use all-around or annular coordinates and I am not abiding which to use, and I don't apperceive how to set up the integrals. Please help!

Answers :Since your artful the aggregate and not the accumulation and don't see what's the role of the body here.

Use annular coordinates:

(Notice in the additional basic starts from z=0, that is I'm just amalgam over bisected of Q and I'm adding by 2 at the start.)

(Here a = √(4^2 - (9/4)^2) = √(175)/4, this is the best z Q reaches)

2∫(from 0 to 2π)∫(from 0 to a)∫(from 9/4 to √(4^2-z^2))(r)drdzdø

=2∫(from 0 to 2π)∫(from 0 to a)∫(from 9/4 to √(4^2-z^2))(r)drdzdø

=2∫(from 0 to 2π)∫(from 0 to a)(1/2)[(4^2-z^2) - (9/4)^2]dzdø
=∫(from 0 to 2π)∫(from 0 to a)[a^2-z^2]dzdø
=∫(from 0 to 2π)[a^3-(1/3)a^3]dø
=(4π/3)a^3

Feel chargeless to ask any questions

here we go
in a quiz game2 prople acknowledgment 100 questions
each getting has answered 90 questions
here is the score
person A has
60% of 90 questions
preson B has
50% of 90 questions
can getting B win this game?
explain your answer
thx