Find the volume of the solid surrounded by two orthogonal cylindrical surfaces whose radii are equal to R The first part of the solution to this problem is to set the equations of two cylindrical surfaces as x ^ 2 + y ^ 2 = R ^ 2 and x ^ 2 + Z ^ 2 = r.. Why?

Because two cylinders intersect vertically, otherwise, they cannot intersect and form a volume
Of course, we can also set X ^ 2 + y ^ 2 = R ^ 2 and Y ^ 2 + Z ^ 2 = R ^ 2

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