Volume and surface area of a cylinder

The problem doesn't specify, but I'm assuming it's the diameter for the volumeIn summary, the conversation is discussing how to find the ratio of volume to area for a cylinder, with the diameter as the given variable. The formula for the volume and area of a cylinder are provided, and simplification is suggested in order to find the desired ratio.
  • #1
Paulo Serrano
52
0

Homework Statement


I need the ratio like in the image below
http://img228.imageshack.us/img228/4015/foiessa.jpg [Broken]
I guess as a function of D.

Homework Equations


Volume of a cylinder: pi*r^2*h
Area: 2*pi*r*(h+r)

The Attempt at a Solution



No clue.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
You have expressions for the area and volume, you are told to compute the ratio

[tex] \frac {Volume} {Area} [/tex]

What is your problem?
 
  • #3
The area of a cylinder, as far as I remember, is: 2*pi*r*h +(2*pi*r^2)
 
  • #4
Now find the the volume, and divide that by area.

V= d^2*pi*h

A= (2*pi*d*h) + (2pi*d^2)

And now write V/A = (d^2*pi*h)/[(2*pi*d*h) + (2pi*d^2)]

I hope I am right, and that it helps! :)
 
  • #5
That is a good start. Now do some simplification.
 
  • #6
d isn't the radius though.
 

1. What is the formula for finding the volume of a cylinder?

The formula for finding the volume of a cylinder is V = πr2h, where π is approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.

2. How do you calculate the surface area of a cylinder?

The formula for calculating the surface area of a cylinder is A = 2πr2 + 2πrh, where π is approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.

3. What units are used to measure volume and surface area of a cylinder?

The volume of a cylinder is usually measured in cubic units (such as cubic centimeters or cubic inches) while the surface area is measured in square units (such as square centimeters or square inches).

4. How does changing the radius or height of a cylinder affect its volume and surface area?

Increasing the radius of a cylinder will result in a larger volume and surface area, while increasing the height will only affect the volume. Similarly, decreasing the radius will result in a smaller volume and surface area, while decreasing the height will only affect the volume.

5. Can the volume and surface area of a cylinder be the same?

No, the volume and surface area of a cylinder cannot be the same. The surface area is the measurement of the curved surface of the cylinder, while the volume is the measurement of the space inside the cylinder. Therefore, the two values will always be different.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
5
Views
1K
  • Precalculus Mathematics Homework Help
Replies
2
Views
3K
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
31
Views
2K
  • Calculus and Beyond Homework Help
Replies
33
Views
2K
  • Thermodynamics
Replies
5
Views
945
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
9
Views
2K
  • Precalculus Mathematics Homework Help
Replies
18
Views
5K
  • Precalculus Mathematics Homework Help
Replies
7
Views
3K
Back
Top