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

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #1 : Solid Geometry

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

Possible Answers:

Correct answer:

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 : Solid Geometry

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

Possible Answers:

Correct answer:

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 .

 

Example Question #3 : Solid Geometry

Possible Answers:

Correct answer:

Explanation:

Example Question #4 : Solid Geometry

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

Possible Answers:

Correct answer:

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 : Solid Geometry

Find the volume of the following cone.

Cone

Possible Answers:

Correct answer:

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 : Solid Geometry

Find the volume of the following cone.

Cone

Possible Answers:

Correct answer:

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 : Solid Geometry

Find the volume of the following half cone.

Half_cone

Possible Answers:

Correct answer:

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 #8 : Solid Geometry

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

Possible Answers:

Correct answer:

Explanation:

The general formula is given by V = 1/3Bh = 1/3\pi r^{2}h, 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?

Possible Answers:

 

Correct answer:

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 #13 : Cones

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?

Possible Answers:

Correct answer:

Explanation:

Cylinder Volume = 

Cone Volume = 

Cylinder Diameter = 6, therefore Cylinder Radius = 3

Cone Radius = 3

Empty Volume = Cylinder Volume – Cone Volume

 

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