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The volume of a volume is the space found inside the cone.

  • Think of the volume as the amount of ice cream you can stuff inside an ice cream cone.


Video answer "Volume of cone."





Problem 3. Find the volume of a cone with a slant height of 9 units and a diameter of 12 units.








Step 1 Find the radius by taking ½ of the diameter
  ½ * 12 =6 units

Step 2 Notice that the slant height is part of a right triangle. Therefore, you can use the Pythagorean Theorem to find your height.







Step 3. 
  • The length of the radius becomes the leg of the right triangle
  • The slant height becomes the hypotenuse of the right triangle
  •  a^2+ 6^2= 9^2







Step 3a a^2+ 36= 81 

Step 3b a^2= 45  

Step 3c  a= √(45 ) this simplifies to 3√5 

Step 4 Plug height into the volume formula 
              1/3*πr^2*h 

Step 4a  1/3*π6^2*3√5

Step 4b  36π* √5 

Step 4c Volume equals 36√5 π units^3 








pythagorean Theorem right triangle
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Volume of a Cone

Pi 4^2 *5 = 80pi/3 Steps for finding volume of a cone
cone volume
Plug your given information into the volume of a cone formula



Problem 2. Find the volume of a cone with a height of 10 and a radius of 6 units.









Step 1.  Plug your numbers into the formula. 
                1⁄3 π6^2*10  

Step 2  Simplify 1⁄3 π6^2*10  

Step 2b  1⁄3 π36*10

Step 3   


Step 3b 12π x 10=120π units^3  ( Please note  volume is always cubed )


inverted cone
volume of a cone
cone that looks like party hat
Volume of a Cone
Finding the volume of a cone is very similar to a cylinder. If you have a cylinder with the same 
radius and height of a cone then you could fit three cones inside the cylinder. Therefore the ratio of a cylinder to a cone is 1 to 3
Let's look at some examples covered in the video.


​5
4
cone
​h
r
h = height of the cone

r = radius of the cone.
Step 1.
Step 2.
The 80 equals (4 squared =16   16 x 5 =80)
Step 3.
Volume of the cone equals 26.6π units^3
right triangle

How do you find the volume of a Cone ?

Formula for volume of a cone equals 1/3 ( base area) ( height)

ice cream cone

Find the volume of a Cone given the slant height.

Video answer "Volume of cone without the height given"

What is the volume of a cone with a radius of 4 and a height of 5?

Begin with the volume formula of a cone.