**Volume of a cone word problems :**

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

In this section, we are going to see, how real-world problems on volume of a cone can be solved.

**Example 1 :**

The height and diameter of a cone-shaped storage tank are 9 feet and 14 feet respectively. Find the volume of liquid the tank can hold. Round your answer to the integer, if necessary. Use the approximate of value of ∏, that is 3.14.

**Solution : **

**Step 1 : **

**Because the tank is in the shape of cone, we can use the formula of volume of a cone to find volume of water the tank can hold.**

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 14 ft. So, find the radius.

r = diameter / 2

r = 14/2

r = 7

**Step 3 : **

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 ≈ 461.58

Round it to the nearest integer.

V ≈ 462

Hence, the volume of the clay is about 462 cubic inches.

**Example 2 :**

A silo is shaped like a cone and contains wheat. The radius is 10 feet and the height is 15 feet. If the silo can release wheat from its bottom at the rate of 25 cubic feet per minute, how long would it take for the silo to empty fully ? Round your answer to the nearest minute. Use the approximate of value of ∏, that is 3.14.

**Solution : **

**Step 1 : **

To know how long it would take for the silo to empty fully, first we have to find the volume of wheat in the silo.

**Because the silo is in the shape of cone, we can use the formula of volume of a cone to find volume of wheat the tank can hold.**

Write the formula to find volume of a cone.

V = 1/3 · ∏r**²**h ----- (1)

**Step 2 : **

Plug ∏ ≈ 3.14, r = 10 and h = 15 in (1).

V ≈ 1/3 · 3.14 · 10² · 15

Simplify.

V ≈ 1/3 · 3.14 · 100 · 15

V ≈ 1,570

So, the volume of wheat in the silo is about 1,570 feet.

**Step 3 : **

Silo can release wheat from its bottom at the rate of 25 cubic feet per minute.

To know how long it would take for the silo to empty 1,570 cubic feet of wheat, divide 1,570 by 25.

= 1,570 / 25

= 62.8 ≈ 63

Hence, it would take about 63 minutes for the silo to empty fully.

After having gone through the stuff given above, we hope that the students would have understood "Volume of a cone word problems".

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