Finding the volume of a cone with a elliptic base

In summary, to find the volume of a cone with an elliptic base, we can use the formula (1/3)*pi*a*b, where a and b are the lengths of the semimajor and semiminor axes of the ellipse. By setting up the problem using the law of similar triangles, we can obtain the values for a and b and then use them in the integral to find the volume.
  • #1
Ahlahn
4
0
Finding the volume of a cone with a elliptic base!

Homework Statement



The area of an ellipse is (pi)ab, where a and b are the lengths of the semimajor and semiminor axes. Compute the volume of a cone of height h = 20 whose base is an ellipse with semimajor and semiminor axes a = 4 and b = 6.

Homework Equations


The Attempt at a Solution



I tried to use the law of similar triangles to obtain the area of the elliptic at the cross section.

4/20 = a/20-y and 6/20 = b/20-y
b=6(20-y)/20 and a = 4(20-y)/20

Since the area of an elliptic is (pi)a*b, I tried to integrate by plugging in the above equations for a and b on the interval [0,20]. I failed.

HELP!
 
Physics news on Phys.org
  • #2


You've set up the problem exactly correctly. The volume is (1/3)*pi*a*b where a=4 and b=6. The integral also gives you (1/3)*pi*a*b where a=4 and b=6. How exactly did you 'fail'?
 

Related to Finding the volume of a cone with a elliptic base

What is the formula for finding the volume of a cone with an elliptic base?

The formula for finding the volume of a cone with an elliptic base is V = (1/3)πabh, where a and b are the lengths of the semi-major and semi-minor axes of the ellipse, and h is the height of the cone.

How is the base of a cone with an elliptic base different from a regular cone?

The base of a cone with an elliptic base is in the shape of an ellipse, while the base of a regular cone is a circle.

Can the volume of a cone with an elliptic base be negative?

No, the volume of a cone with an elliptic base cannot be negative as it represents the amount of space enclosed by the cone and is always a positive value.

What units should be used when finding the volume of a cone with an elliptic base?

The units used for the lengths of the semi-major and semi-minor axes and the height should all be the same. The resulting volume will be in cubic units, such as cubic inches or cubic centimeters.

What is the significance of finding the volume of a cone with an elliptic base?

Finding the volume of a cone with an elliptic base can be useful in various real-world applications, such as calculating the volume of an ice cream cone, determining the capacity of a cone-shaped container, or estimating the volume of a volcano based on its elliptical shape.

Similar threads

  • Calculus and Beyond Homework Help
Replies
3
Views
613
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
9
Views
2K
  • Calculus and Beyond Homework Help
Replies
5
Views
717
  • Calculus and Beyond Homework Help
Replies
10
Views
1K
  • Calculus and Beyond Homework Help
Replies
17
Views
4K
  • Calculus and Beyond Homework Help
Replies
3
Views
822
  • Calculus and Beyond Homework Help
Replies
4
Views
968
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
Back
Top