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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

**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 )

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.

h = height of the cone

r = radius of the cone.

The 80 equals (4 squared =16 16 x 5 =80)

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.