**Finding the volume of a sphere :**

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

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

Volume of cone = 2/3 · Volume of cylinder

Substitute the formula for volume of cylinder.

Volume of the cone = 2/3 · ∏r**²**h

A sphere always has a height which is equal to twice the radius.

So, substitute 2r for h.

Volume of sphere = 2/3 · ∏r²(2r)

Simplify.

Volume of sphere = 4/3 · ∏r³

**Example 1 :**

Find the volume of the sphere 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 sphere.

V = 4/3 · ∏r³

**Step 2 : **

Substitute the given measures.

V ≈ 4/3 · 3.14 · 2.2³

Simplify.

V ≈ 4/3 · 3.14 · 10.648

V ≈ 44.6

Hence, the volume of the given sphere is about 44.6 cubic cm.

**Example 2 :**

Find the volume of the sphere 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 sphere.

V = 4/3 · ∏r³ ----- (1)

**Step 2 : **

To find the volume, we need the radius of the sphere. But, the diameter is given, that is 42 cm. So, find the radius.

r = diameter / 2

r = 42/2

r = 21

**Step 3 : **

Plug ∏ ≈ 3.14 and r = 21 in (1).

V ≈ 4/3 · 3.14 · 21³

Simplify.

V ≈ 4/3 · 3.14 · 9261

V ≈ 38,772.7

Hence, the volume of the given sphere is about 38,772.7 cubic cm.

**Example 3 :**

Find the volume of the sphere 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 sphere.

V = 4/3 · ∏r³ ----- (1)

**Step 2 : **

To find the volume, we need the radius of the sphere. But, the height is given, that is 12 cm.

We know that the height of a sphere equals twice the radius.

That is,

h = 2r

Plug h = 12.

12 = 2r

Divide both sides by 2.

12/2 = 2r/2

6 = r

**Step 3 : **

Plug ∏ ≈ 3.14 and r = 6 in (1).

V ≈ 4/3 · 3.14 · 6³

Simplify.

V ≈ 4/3 · 3.14 · 216

V ≈ 904.3

Hence, the volume of the given sphere is about 904.3 cubic cm.

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