Find the area of the following surfaces using an explicit description of the surface. The paraboloid z=2(x2+y2), for 0<=z<=8.

68.47

Step-by-step explanation:

Given that:

The surface of the paraboloid

TO find the area of the given paraboloid, we need to first determine .

This is because the surface area can be determined by using the formula:

Thus;

Now;

Using the polar coordinate since the paraboloid shows the projection of a circle with

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

okay..i will pick 8!