Find the area of the surface. The part of the surface z = xy that lies within the cylinder x^2 + y^2 = 9

The area of surface is

Step-by-step explanation:

Given that,

The equation of cylinder is

The part of the surface z = xy

The coordinates is,

We need to calculate the value of ds

Using formula of ds

Put the value in to the formula

....(I)

We know that.

The polar coordinates,

The general equation of cylinder is

compare from given equation

0<=θ<=2π, 0<=r<=3

Area element in polar coordinates is,

Put the value of dA in equation (I)

....(II)

We need to calculate the area of surface

Using equation (II)

Hence, The area of surface is

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step-by-step explanation: