# High School Math : How to find the volume of a cone

## Example Questions

### Example Question #1 : Cones

What is the volume of a cone with a height of  and a base with a radius of ?

Explanation:

To find the volume of a cone we must use the equation . In this formula, is the area of the circular base of the cone, and is the height of the cone.

We must first solve for the area of the base using .

The equation for the area of a circle is . Using this, we can adjust our formula and plug in the value of our radius.

Now we can plug in our given height, .

Multiply everything out to solve for the volume.

The volume of the cone is .

### Example Question #2 : Cones

What is the equation of a circle with a center of (5,15) and a radius of 7?

Explanation:

To find the equation of a circle we must first know the standard form of the equation of a circle which is

The letters  and  represent the -value and -value of the center of the circle respectively.

In this case  is 5 and k is 15 so plugging the values into the equation yields

We then plug the radius into the equation to get

Square it to yield

The equation with a center of (5,15) and a radius of 7 is .

Explanation:

### Example Question #1 : Cones

What is the volume of a cone that has a radius of 3 and a height of 4?

Explanation:

The standard equation for the volume of a cone is

where  denotes the radius and  denotes the height.

Plug in the given values for  and  to find the answer:

### Example Question #5 : Cones

Find the volume of the following cone.

Explanation:

The formula for the volume of a cone is:

where  is the radius of the cone and  is the height of the cone.

In order to find the height of the cone, use the Pythagorean Theorem:

Plugging in our values, we get:

### Example Question #6 : Cones

Find the volume of the following cone.

Explanation:

The formula for the volume of a cone is:

Where  is the radius of the cone and  is the height of the cone

Use the Pythagorean Theorem to find the length of the radius:

Plugging in our values, we get:

### Example Question #7 : Cones

Find the volume of the following half cone.

Explanation:

The formula of the volume of a half cone is:

Where  is the radius of the cone and  is the height of the cone.

Use the Pythagorean Theorem to find the height of the cone:

### Example Question #1 : How To Find The Volume Of A Cone

What is the volume of a right cone with a diameter of 6 cm and a height of 5 cm?

Explanation:

The general formula is given by , where  = radius and  = height.

The diameter is 6 cm, so the radius is 3 cm.

### Example Question #1 : How To Find The Volume Of A Cone

There is a large cone with a radius of 4 meters and height of 18 meters. You can fill the cone with water at a rate of 3 cubic meters every 25 seconds. How long will it take you to fill the cone?

Explanation:

First we will calculate the volume of the cone

Next we will determine the time it will take to fill that volume

We will then convert that into minutes

### Example Question #1 : How To Find The Volume Of A Cone

You have an empty cylinder with a base diameter of 6 and a height of 10 and you have a cone full of water with a base radius of 3 and a height of 10.  If you empty the cone of water into the cylinder, how much volume is left empty in the cylinder?

Explanation:

Cylinder Volume =

Cone Volume =

Cylinder Diameter = 6, therefore Cylinder Radius = 3

Cone Radius = 3

Empty Volume = Cylinder Volume – Cone Volume