High School Math : Geometry

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #2 : Cones

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : 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 #3 : 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 #4 : 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 #1 : Cones

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 #1 : 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 #3 : 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?

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

 

Example Question #11 : Solid Geometry

What is the volume of a cone with base radius 4, and height 6?

Possible Answers:

Correct answer:

Explanation:

The volume of a cone is  , where  is the height of the cone and  is the base radius.

The volume of this cone is thus:

=  

Example Question #541 : Geometry

What is the surface area of a cone with a radius of 4 and a height of 3?

Possible Answers:

25\pi

40\pi

36\pi

16\pi

48\pi

Correct answer:

36\pi

Explanation:

Here we simply need to remember the formula for the surface area of a cone and plug in our values for the radius and height.

\Pi r^{2} + \Pi r\sqrt{r^{2} + h^{2}}= \Pi\ast 4^{2} + \Pi \ast 4\sqrt{4^{2} + 3^{2}} = 16\Pi + 4\Pi \sqrt{25} = 16\Pi + 20\Pi = 36\Pi

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