Calculating Arc Length and Area of Cylinder Side

In summary, the conversation discusses a cylinder with a given radius and a specific portion of the cylinder. The length of an arc and a line segment are expressed in terms of the radius and angle, and the area of a side of the cylinder is calculated and expressed in terms of the radius. A sketch is recommended to better understand the problem.
  • #1
help
14
0

Homework Statement

Let r be a positive constant. [/B]
Consider the cylinder x2 + y2 ≤ r2, and let C be the part of the cylinder that satisfies 0 ≤ z ≤ y.

(3) Let a be the length of the arc along the base circle of C from the point (r, 0, 0) to the point (r cos θ, r sin θ, 0) (0 ≤ θ ≤ π). Let b be the length of the line segment from the point (r cos θ, r sin θ, 0) to the point (r cos θ, r sin θ, r sin θ). Express a and b in terms of r, θ. (
4) Calculate the area of the side of C with x2+y2 = r2, and express it in terms of r.

Homework Equations

[/B]
Not sure

The Attempt at a Solution



I used the formula[/B]

image045.gif
.

[f '(x)]² = x²/(r²-x²)

... r∫π0dθ=? the answer ir θr
 

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  • #2
Hello help, :welcome:

Make a sketch. For ##a## it can even be a simple 2D sketch.
 

Related to Calculating Arc Length and Area of Cylinder Side

1. What is the formula for calculating the arc length of a cylinder side?

The formula for calculating the arc length of a cylinder side is 2πr, where r is the radius of the cylinder.

2. How is the area of a cylinder side calculated?

The formula for calculating the area of a cylinder side is 2πrh, where r is the radius of the cylinder and h is the height of the cylinder.

3. Can I use the same formula to calculate the arc length and area of any cylinder side?

Yes, the formula 2πr can be used to calculate both the arc length and area of any cylinder side, as long as the radius remains constant.

4. What units should I use for the measurements in the formula?

The units used for the measurements in the formula should be consistent. For example, if the radius is measured in inches, then the arc length and area should also be calculated in inches.

5. Is there a difference between the arc length and circumference of a cylinder side?

Yes, there is a difference between the arc length and circumference of a cylinder side. The arc length refers to the length of the curved portion of the cylinder, while the circumference refers to the length of the entire circular base of the cylinder.

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