**How to find the volume of a volcano : **

The mountain created by a volcano is usually cone–shaped.

Because volcano is usually cone-shaped, we can use the formula of volume of a cone to find the volume of a volcano.

Volume of a cone = 1/3 · ∏r**²**h

So,

Volume of a volcano = 1/3 · ∏r**²**h

**Example 1 :**

For her geography project, Alex built a clay model of a volcano in the shape of a cone. His model has a diameter of 14 inches and a height of 9 inches. Find the volume of clay in his model to the nearest tenth. Use the approximate of value of ∏, that is 3.14.

**Solution : **

**Step 1 : **

Write the formula to find volume of a volcano.

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 14 inches. So, find the radius.

r = diameter / 2

r = 14/2

r = 7

**Step 2 : **

Plug ∏ ≈ 3.14, r = 7 and h = 9 in (1).

V ≈ 1/3 · 3.14 · 7² · 9

Simplify.

V ≈ 1/3 · 3.14 · 49 · 9

V ≈ 461.6

Hence, the volume of the clay is about 461.6 cubic inches.

**Example 2 :**

The cone of the volcano Paricutin in Mexico had a height of 410 meters and a diameter of 424 meters. Find the volume of the cone to the nearest tenth. 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 424 meters. So, find the radius.

r = diameter / 2

r = 424/2

r = 212

**Step 2 : **

Plug ∏ ≈ 3.14, r = 212 and h = 410 in (1).

V ≈ 1/3 · 3.14 · 212² · 410

Simplify.

V ≈ 1/3 · 3.14 · 44944 · 410

V ≈ 19,286,968.5

Hence, the volume of the cone is about 19,286,968.5 cubic meters.

After having gone through the stuff given above, we hope that the students would have understood, how to find the volume of a volcano.

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