Suppose we have a solid S that is bounded by the following surfaces:
z = 5x^2 + 5y^2 and z = 28 - 2x^2 - 2y^2
1.) Determine the surface area of S.
2.) Determine the avg. distance from the z-axis to a point in S.
Could someone please check my work!
5x^2 + 5y^2 = 28 - 2x^2 - 2y^2
7x^2 + 7y^2 = 28
y = +/- sqrt(4-x^2) . . . z = 20
z = 5x^2 + 5y^2
f_x = 10x = 10*r*cos(theta)
f_y = 10y = 10*r*sin(theta)
z = 28 - 2x^2 - 2y^2
f_x = -4x = -4*r*cos(theta)
f_y = -4y = -4*r*sin(theta)
SA = int(int_R(sqrt(f_(x)^2 = f_(y)^2 + 1)dA
int(int(sqrt(16r^2*cos^2(theta) + 16r^2*sin^2(theta) + 1)r dr d(theta)..
Note the limits of integration are, respectively, 0 to 2Pi, 0 to 2..
I did it out and got 172.6 ...
PLEASE would someone help me determine if this is right.
For the avg. distance I'm not sure.
And how do they intersect? Note:
5x^2+5y^2 = 28 - 2x^2 - 2y^2
7x^2+7y^2 = 28
x^2 +y^2 = 4
That is they intersect in a circle centered at origin or radius 2.
Now follow attachment.