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In this lesson, we will learn about the volume of a cylinder.

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Let’s start, consider this circle with the radius r.

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By now, we should already know that the area, A, of this circle is pi r square.

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Next, let's change this circle into a cylinder.

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After doing so, this cylinder has the radius r, and the height h.

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Now, to find the volume of this cylinder, V, we just multiply the area, A with the height, h.

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Hence, we multiply pi r square, with h.

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This gives the formula for the volume of a cylinder, V equal pi r square h.

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Now, it is important that we include the unit for volume.

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Since the unit is not given, we can write the unit as cubic unit.

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Alright, let's see some examples on finding the volume of a cylinder. For these examples, we take pi as 3.14.

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Find the volume of this cylinder which has the radius 3cm and the height 5cm.

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Let's start by using the formula, V equal pi r square h.

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Now, since the radius is given as 3 cm, we can substitute 'r' with 3.

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Next, let's simplify 3 square. Here, we can see that 3 square equals to 3 multiply by 3. This gives 9. Let's write this down here.

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Let's continue. The height h is given as 5 cm. Hence, we can substitute h with 5.

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Now, we can simplify this equation by multiplying 9 with 5. This gives 45.

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Next, pi is given as 3.14. So, let's substitute pi with 3.14.

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Finally, we can find the volume by multiplying 3.14 with 45. This gives 141.30.

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Note that, this number has no meaning unless we include the unit for it.

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Since the radius and height are in centimeter, the volume will be in cubic centimeter.

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Hence, the volume of this cylinder is 141.30 cubic centimeter.

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Next example, the volume of this cylinder is 50 cubic ft and its radius is 2ft. Find its height, h.

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Now, let's begin with the formula, V = pi r square h.

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Since the volume of the cylinder is given as 50, we can substitute V with 50.

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Next, since the radius is given as 2, we can substitute r with 2.
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Now, let's simplify 2 square. 2 square is actually, 2 multiply by 2 which is equals to 4. Let's write this down here.

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Next, we can substitute pi with 3.14.

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Here, we can simplify this equation by multiplying 3.14 with 4.

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This gives 12.56.

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Now, we have 12.56 h equals to 50. Let's rewrite this equation so it will be easier to see.

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Next, to solve for 'H', we divide both sides of the equation with 12.56.

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This gives, h equals to, 50 divided by 12.56.

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Now, we can find h by dividing 50 with 12.56. This gives 3.98.

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Again, this number has no meaning unless we include the unit for it.

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Since the radius is in feet, the height of the cylinder will also be in feet.

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Hence, the height of the cylinder is 3.98 ft.

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That is all for this lesson. Try out the practice question to test your understanding.