Find the area of the finite part of the paraboloid y = x2 + z2 cut off by the plane y = 25. [Hint: Project the surface onto the xz-plane.]
To find: The area of the given region.
The surface area with equation , where and are continuous, is .
Here, D is the given region.
If is a polar rectangle R given by where , then, (1)
If is the function of and is the function of then,
The finite part of the paraboloid, cutoff by the plane .
From the hint given in the problem, project the region onto the xz-plane that is substitute in . This yields, which means in xz-plane, the region is the circle of radius 5. So, use polar coordinates to evaluate the area of the region.
The partial derivatives and are,
Then, by the formula mentioned above, the area of the surface is given by,
Since the equation involves only x and z, substitute
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