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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
Volume of a Cone
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 )
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
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
How do you find the volume of a Cone ?
Formula for volume of a cone equals 1/3 ( base area) ( height)
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.