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 · πr²h cubic units

So,

Volume of a volcano  =  1/3 · πr²h cubi units

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 π, that is 3.14. 

Solution : 

Step 1 : 

Write the formula to find volume of a volcano.

V  =  1/3 · πr²h -----(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 : 

Substitute π ≈ 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

So, 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 π, that is 3.14. 

Solution : 

Step 1 : 

Write the formula to find volume of a cone.

V  =  1/3 · πr²h -----(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 : 

Substitute π ≈ 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

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

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