# Finding the volume of a cone with a elliptic base

• Ahlahn
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.
Ahlahn
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.

## 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!

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'?

## 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.

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