Use cylindrical coordinates. Find the volume of the solid that lies within both the cylinder x2 y2

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Use cylindrical coordinates Find the volume of the solid that lies within both the cylinder x^2 + y^2=16 and the sphere x^2 + y^2 + Z^2= 81

Answer :

Step-by-step explanation:

The given data

cylinder  = x^2 + y^2 = 16

sphere = x^2 + y^2 +z^2 = 81

from the given data the solid is symmetric around the xy plane hence we will calculate half the solid volume above the plane then  multiply the sesult by 2

Note : we are restricting our attention to the cylinder  x^2 + y^2 = 16 and also finding the volume inside the sphere which gives bound on the z-coordinate as well

the r parameter goes from 0 to 4

ATTACHED IS THE REMAINING PART OF THE SOLUTION

showing the integration

b

step-by-step explanation: