Find Surface Area of Sphere Part Above xy-Plane & Within Cylinder

In summary, the formula for finding the surface area of a sphere is 4πr², the formula for finding the surface area of the part of a sphere above the xy-plane is 2πrh, the formula for finding the surface area of a cylinder is 2πrh + 2πr², and to find the surface area of the part of a sphere within a cylinder, you can subtract the surface area of the part outside the cylinder from the total surface area of the sphere. This can be done using the formula 4πr² for the entire sphere and 2πrh for the part outside the cylinder. Additionally, the same formula, 4πr², can be used to find the surface
  • #1
naspek
181
0
Find the surface area of that portion of the sphere x^2 + y^2 + z^2 = a^2 that is above xy-plane and within the cylinder x^2 + y^2 = b^2 , 0 < b < a

Solution.. i try to find fx and fy..

http://imageshack.us/f/594/33049204.jpg/"

how am i going to proceed?
 
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  • #2
It would be very simple with spherical polar coordinates.

ehild
 

Related to Find Surface Area of Sphere Part Above xy-Plane & Within Cylinder

What is the formula for finding the surface area of a sphere?

The formula for finding the surface area of a sphere is 4πr², where r is the radius of the sphere.

How do I find the surface area of the part of a sphere above the xy-plane?

To find the surface area of the part of a sphere above the xy-plane, you can use the formula 2πrh, where r is the radius of the sphere and h is the height of the portion above the xy-plane.

What is the formula for finding the surface area of a cylinder?

The formula for finding the surface area of a cylinder is 2πrh + 2πr², where r is the radius of the base and h is the height of the cylinder.

How do I find the surface area of the part of a sphere within a cylinder?

To find the surface area of the part of a sphere within a cylinder, you can first calculate the surface area of the entire sphere using the formula 4πr² and then subtract the surface area of the part outside the cylinder, which can be found using the formula 2πrh.

Can I use the same formula to find the surface area of any sphere?

Yes, the formula for finding the surface area of a sphere, 4πr², can be used to find the surface area of any sphere, regardless of its size or position.

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