**Finding the volume of a cone :**

We can find the volume of a cone using the formula of volume of a cylinder.

When we model the volume of a cone, we will be getting the following result.

Volume of cone = 1/3 · Volume of cylinder

Substitute the formula for volume of cylinder.

Volume of the cone = 1/3 · ∏r**²**h cu. units

**Example 1 :**

Find the volume of the cone given below. Round your answer to the nearest tenth if necessary. Use the approximate of value of ∏, that is 3.14.

**Solution : **

**Step 1 : **

Write the formula to find volume of a cone.

V = 1/3 · ∏r**²**h

**Step 2 : **

Substitute the given measures.

V ≈ 1/3 · 3.14 · 2² · 8

Simplify.

V ≈ 1/3 · 3.14 · 4 · 8

V ≈ 33.5

Hence, the volume of the given cone is about 33.5 cubic inches.

**Example 2 :**

Find the volume of the cone given below. Round your answer to the nearest tenth if necessary. Use the approximate of value of ∏, that is 3.14.

**Solution : **

**Step 1 : **

Write the formula to find volume of a cone.

V = 1/3 · ∏r**²**h ----- (1)

**Step 2 : **

To find the volume, we need the radius of the cone. But, the diameter is given, that is 8 ft. So, find the radius.

r = diameter / 2

r = 8/2

r = 4

**Step 3 : **

Plug ∏ ≈ 3.14, r = 4 and h = 9 in (1).

V ≈ 1/3 · 3.14 · 4² · 9

Simplify.

V ≈ 1/3 · 3.14 · 16 · 9

V ≈ 150.7

Hence, the volume of the given cone is about 150.7 cubic feet.

**Example 3 :**

Find the volume of the cone given below. Round your answer to the nearest tenth if necessary. Use the approximate of value of ∏, that is 3.14.

**Solution : **

**Step 1 : **

Write the formula to find volume of a cone.

V = 1/3 · ∏r**²**h ----- (1)

**Step 2 : **

To find the volume, we need the radius of the cone. But, the diameter is given, that is 15 cm. So, find the radius.

r = diameter / 2

r = 15/2

r = 7.5

**Step 3 : **

Plug ∏ ≈ 3.14, r = 7.5 and h = 16 in (1).

V ≈ 1/3 · 3.14 · 7.5² · 16

Simplify.

V ≈ 1/3 · 3.14 · 56.25 · 16

V ≈ 942

Hence, the volume of the given cone is about 942 cubic cm.

**Example 4 :**

**Solution : **

**Step 1 : **

Write the formula to find volume of a cone.

V = 1/3 · ∏r**²**h

**Step 2 : **

Substitute the given measures.

V ≈ 1/3 · 3.14 · 2² · 3

Simplify.

V ≈ 1/3 · 3.14 · 4 · 3

V ≈ 12.6

Hence, the volume of the given cone is about 12.6 cubic feet.

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