Compute the surface area of the portion of the sphere with center the origin and radius 4 that lies inside the cylinder x^2+y^2=12

16π

Step-by-step explanation:

Given that:

The sphere of the radius =

The partial derivatives of

Similarly;

∴

Now; the region R = x² + y² = 12

Let;

x = rcosθ = x; x varies from 0 to 2π

y = rsinθ = y; y varies from 0 to

dA = rdrdθ

∴

The surface area

= 8π ( -2 + 4)

= 8π(2)

= 16π

47

step-by-step explanation:

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