- #1

s_engineering

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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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- Thread starter s_engineering
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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

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

tiny-tim

Science Advisor

Homework Helper

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Hi s_engineering! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

- #3

s_engineering

- 2

- 0

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.

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.

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.

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.

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.

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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