Calculate the volume enclosed by the sphere of radius centered at the origin and the circular cylinder x^2 + y^2 = x. Remember that the mass of a solid E is obtained by the formula

where f is the mass density function and dV is the volume differential.

Also,

i) Decide what type of coordinates to use and why. (There may be an exercise in which two or three types of coordinates work well, although generally one is the most suitable.)

(ii) Make a drawing or drawings that illustrate what is happening.A three-dimensional drawing and also a projection or cross section may be convenient.

(iii) The limits of the iterated integrals.

(iv) The calculations as such. Be alert to symmetries that can simplify the accounts.

SSI fav E SSI fav E