Surface Area of Cylinder Bounded by x^2 + y^2 = a^2

In summary, the conversation is about finding the surface area of the portions of a cylinder bounded by two equations. The person has tried setting up a double integral using polar coordinates but is unsure of the boundaries to use. They ask for help and are encouraged to show their work and where they are stuck.
  • #1
s_engineering
2
0
Find the surface area of the the portions of the cylinder y^2 + z^2=a^2 bounded by x^2 + y^2 = a^2


not really sure how to go about this. tried to set up a double integral and use polar coordinates but don't know what boundaries to use etc.
 
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  • #2
Welcome to PF!

Hi s_engineering! Welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3
this is what I've tried:

fy = 2y; fz=2z

A(S)=int int sqrt{1+4y^2 +4z^2}dA

then I switched to polar coordinates i tired to integrate from theta=0 to pi/2 and r= 0 to a
but didn't get anywhere with this.
 

FAQ: Surface Area of Cylinder Bounded by x^2 + y^2 = a^2

1. What is the formula for finding the surface area of a cylinder bounded by x^2 + y^2 = a^2?

The formula for finding the surface area of a cylinder bounded by x^2 + y^2 = a^2 is 2πar, where r is the radius of the cylinder and a is the radius of the base circle.

2. How is the surface area of a cylinder bounded by x^2 + y^2 = a^2 related to its volume?

The surface area of a cylinder bounded by x^2 + y^2 = a^2 is not directly related to its volume. However, the surface area can be used to calculate the volume by using the formula V = πr^2h, where r is the radius of the base and h is the height of the cylinder.

3. Can the surface area of a cylinder bounded by x^2 + y^2 = a^2 be greater than its volume?

No, it is not possible for the surface area of a cylinder bounded by x^2 + y^2 = a^2 to be greater than its volume. The surface area will always be equal to or less than the volume.

4. How does changing the radius of the base affect the surface area of a cylinder bounded by x^2 + y^2 = a^2?

Changing the radius of the base will directly affect the surface area of a cylinder bounded by x^2 + y^2 = a^2. As the radius increases, the surface area will also increase, and vice versa.

5. Is there a difference in the surface area between a cylinder bounded by x^2 + y^2 = a^2 and a regular cylinder with the same dimensions?

No, there is no difference in the surface area between a cylinder bounded by x^2 + y^2 = a^2 and a regular cylinder with the same dimensions. The formula for calculating the surface area is the same for both types of cylinders.

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