Volume of a Cylinder

Volume of a cylinder is in other words the capacity of the shape, with the assumption that its walls are extremely thin. It is often expressed in cubic meters (m³) or cubic centimeters (cm³) (1 cm³ = 1 ml). In everyday life it is easier to find the use of liter unit, which is equivalent to 1,000 cm³. A standard sized can used by most of the fizzy drinks manufacturers is in approximation a cylinder with capacity of 330 ml = ⅓ of a liter.

Now when we know what the volume of a cylinder is it would be good to know how to calculate it without the necessity of filling it up with liquid. The calculation turns out to be quite straightforward and requires calculating the area of a circle that forms the base of a cylinder and multiplying the result by the height of that cylinder.

In the similar way we can calculate the volume of a regular shape where the base (and top) instead of a circle is formed by square, rectangle, triangle etc. The principle there stays the same and calculating the volume requires multiplying the area of the base by the height of the shape. Therefore a volume of a cube will be easily calculated by multiplying the area of the base by the height of the cube.

Exercise 1.

How much water is needed to fill up a barrel of 1 meter high, with base having 50cm in diameter.

Solution: First thing we need to do is unify the units used in our exercise. Therefore 50 cm is 0.5 of a meter. As we will need the radius of the base to calculate its area we divide the diameter by 2 to achieve 0.25 m. Now we have all the variables to be able to solve our problem:

This way we have calculated that the volume of the given cylinder is 0.19625 m3. To be able to picture more easily how much water it actually is let’s convert that value to liters. We said before that 1 liter is equal to 1000 cm³, so let’s try to convert our cubic meters to cubic centimeters. 1 cubic meter is equal to 100 cm * 100 cm * 100 cm which is 1,000,000 cm³. Multiplying that value by the result of our calculation we get the volume of our barrel in cubic centimeters: 196,250 cm3. Now if we divide that by the number of cubic centimeters in a liter we get that it takes 196.25 liters of water to fill up our barrel.

Exercise 2.

An interesting exercise would be to try to find out what the dimensions of a cylinder have to be for its volume to be equal to 1. There is infinite number of correct answers to that question. The volume of 1 can be achieved with many cylinder dimensions by adjusting the height and the diameter of the base circle.

An easy setup to start with would be to take a circle with area of 1 as a base of our cylinder. Then growing the shape to the shape of 1 would produce the required result. What should be the radius of the circle for its area to be 1? Let’s use the area of a circle equation to calculate that:

Now we know that for the cylinder of the height of 1 unit to have a volume of 1 cubic unit radius of its base needs to be 0.56 o a unit.