**Finding the volume of a cylinder :**

Finding volumes of cylinders is similar to finding volumes of prisms. We can find the volume V of both a prism and a cylinder by multiplying the height by the area of the base.

Let the area of the base of a cylinder be B and the height of the cylinder be h. Write a formula for the cylinder’s volume V.

V = Bh

The base of a cylinder is a circle, so for a cylinder,

B = ∏r**²**

Then, we have

**V = ∏r²h **cubic units

**Example 1 :**

Find the volume of the cylinder 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 cylinder

V = ∏r**²**h cubic units

**Step 2 : **

Substitute the given measures.

V ≈ 3.14 · 3² · 10

Simplify.

V ≈ 3.14 · 9 · 10

V ≈ 282.6

Hence, the volume of the given cylinder is about 282.6 cubic inches.

**Example 2 :**

Find the volume of the cylinder 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 cylinder

V = ∏r**²**h cubic units ---- (1)

**Step 2 : **

To find the volume, we need the radius of the cylinder. But, the diameter is given, that is 6.4 cm. So, find the radius.

r = diameter / 2

r = 6.4/2

r = 3.2

**Step 3 : **

The given cylinder is in horizontal position and its length is 13 cm. If the cylinder is in vertical position, the length will become height. So, the height is

h = 13

**Step 4 :**

Plug ∏ ≈ 3.14, r = 3.2 and h = 13 in (1).

V ≈ 3.14 · 3.2² · 13

Simplify.

V ≈ 3.14 · 10.24 · 13

V ≈ 418

Hence, the volume of the given cylinder is about 418 cubic cm.

**Example 3 :**

Find the volume of the cylinder 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 cylinder

V = ∏r**²**h cubic units ---- (1)

**Step 2 : **

The given cylinder is in horizontal position and its length is 12 ft. If the cylinder is in vertical position, the length will become height. So, the height is

h = 12

**Step 3 : **

Plug ∏ ≈ 3.14, r = 4 and h = 12 in (1).

V ≈ 3.14 · 4² · 12

Simplify.

V ≈ 3.14 · 16 · 12

V ≈ 602.9

Hence, the volume of the given cylinder is about 602.9 cubic feet.

**Example 4 :**

**Solution : **

**Step 1 : **

Write the formula to find volume of a cylinder

V = ∏r**²**h cubic units ---- (1)

**Step 2 : **

To find the volume, we need the radius of the cylinder. But, the diameter is given, that is 10 cm. So, find the radius.

r = diameter / 2

r = 10/2

r = 5

**Step 2 : **

Plug ∏ ≈ 3.14, r = 5 and h = 6 in (1).

V ≈ 3.14 · 5² · 6

Simplify.

V ≈ 3.14 · 25 · 6

V ≈ 471

Hence, the volume of the given cylinder is about 471 cubic inches.

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