# Calculate Volume of a Cone: Formulas & Steps

• Ruturaj Vaidya
In summary: I think you are misunderstanding what the problem is and what the given formulas are.In summary, the formulas required for this problem are the area of a circle and the volume of a cone. The height of the larger cone is not 15 meters, it is actually 30 meters. To calculate the volume of the fiber composite needed, the volume of the outer portion of the cone and the volume of the inside, which is also a frustum of a cone, must be found. However, the calculations done by the person asking for help are incorrect and do not involve the correct formulas. The solution can be found by using only the formula for the volume of a cone.
Ruturaj Vaidya
The required Formulas are:

Area of circle = Pi (r)^2

Volume of Cone = 1/3 Pi (r)^2 h

Here is my try:

I know the smaller cone and bigger ones are congurent, so

50/25 = 15/h

Ruturaj Vaidya said:
50/25 = 15/h
This is not correct: the height of the bigger cone is not 15.

Yes, thanks, I have realized that . The total height is 30m. However, I can't calculate the volume of fiber composite needed?

Ruturaj Vaidya said:
Yes, thanks, I have realized that . The total height is 30m. However, I can't calculate the volume of fiber composite needed?
You need the formula for the volume of a frustum of a cone. Find the volume of the outer portion of the cone, and then find the volume of the inside, which is also a frustum of a cone, but a little bit smaller.

Yes, I have tried that, but that does not work either :(

Ruturaj Vaidya said:
Yes, I have tried that, but that does not work either :(
Why do you think it doesn't work. Please show us what you did.

Here is what I did:

I found that the net of the cone are basically two rings (for the composite fiber) and a trapezium)for the curved surface.
It is a three dimensional trapezium, so I multiplied the trapezium's area by the width (2.5cm). I subtracted the volume of the larger trapezium prism with that of the smaller trapezium prism, to gain the composite fiber volume. Here is my working:

However, the answer is ridiculously large, and even when I don't add the area of the circles (as seen above), the answer remains large. The solutions sheet says that the answer is closer to 8.67 cm^3

You have the height of a cone measured in meters.
You have the diameter of the cone measured in centimeters.
You have the thickness of the composite measured in millimeters.

So naturally, you just throw all of these different units into a giant crank and expect volume in cubic centimeters to emerge automatically.

IDK what you are doing using the formula for volume of a three dimensional trapeze-whatever.

This problem can be solved knowing the formula for the volume of a cone and only that formula.

Ruturaj Vaidya said:
Here is what I did:

I found that the net of the cone are basically two rings (for the composite fiber) and a trapezium)for the curved surface.
It is a three dimensional trapezium, so I multiplied the trapezium's area by the width (2.5cm). I subtracted the volume of the larger trapezium prism with that of the smaller trapezium prism, to gain the composite fiber volume. Here is my workingowever, the answer is ridiculously large, and even when I don't add the area of the circles (as seen above), the answer remains large. The solutions sheet says that the answer is closer to 8.67 cm^3
You really have things confused here. The image you showed has a trapezoidal shaped solid that has nothing to do with this problem, and you mentioned "area of circles" above.

## What is the formula for calculating the volume of a cone?

The formula for calculating the volume of a cone is V = (1/3)πr2h, where r is the radius of the base and h is the height of the cone.

## How do you find the radius of a cone?

The radius of a cone can be found by measuring the distance from the center of the base to the edge of the base. Alternatively, if the diameter of the base is known, the radius can be found by dividing the diameter by 2.

## What is the unit of measurement for volume?

The unit of measurement for volume is typically cubic units, such as cubic centimeters (cm3) or cubic meters (m3).

## What is the difference between a cone and a cylinder?

A cone has a circular base and a curved surface that tapers to a point, while a cylinder has two parallel circular bases connected by a curved surface. Additionally, the volume formula for a cone includes a factor of 1/3, while the volume formula for a cylinder does not.

## Can the volume of a cone be negative?

No, the volume of a cone cannot be negative. Volume is a measure of the amount of space an object occupies and cannot be negative. If the calculated volume is negative, it is likely due to an error in measurement or calculation.

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