Volume of a Cylinder

I was never a big fan of Geometry. In fact, the word 'geometry' itself brings with it a feeling of dread which I can barely push back. But now, I say this as someone who is not too fond of math, that mensuration is one of the simplest chapters you will find in this subject. Why? Simple. Mensuration is based on formulas. So as long as you mug up the simple formulas for area of circles and volume of a cylinder and of other different shapes, you're good to go! So I will always say this, that even if you suck at Geometry and mathematics, do the mensuration chapter well! But then again, wouldn't it be better if you knew how and why the formula came about? Problem solving becomes so easier!

Equation for the Volume

A cylinder is a three dimensional geometric figure, not unlike your normal soda can. It has a rounded surface and is bound by two circular surfaces on its top and bottom. What is volume? A volume is something quite specific to three dimensional figures, and refers to the space contained on the inside of such a figure. Why do we calculate the volume of a geometric figure? Often we need to know how much of a solid, liquid, or gaseous matter a container can contain. Taking the example of the soda can further, suppose you want to know how much soda a cylinder of certain measurements can contain, you simply insert the measurements of the cylinder into the formula and you have your answer!

Look at the cylinder carefully. What do you see? You see a figure of a specific height which is bounded by a couple of circles. And that's how you get to deriving the formula. You know that the formula for the area of a circle is πr². But this surface has a height. So putting these two things together, you get the formula for the volume of a cylinder i.e. πr²h, where 'r' is the radius of the two circles on each side of the cylinder and 'h' is the height of the cylinder.

Calculating the Volume

Suppose you have a cylinder whose radius is 10 in and height is 14 in. Simply substitute the values in the formula:

πr²h

= 22/7 * 10² * 14

= 4400.

We all know that the unit in which the area is given is known or written as the square of the unit. The unit for denoting the volume is written as the cube of the units in which it is measured. So since the above example had the height and radius of the cylinder measured in cm, the unit which denotes the volume is called in³ or cubic inches. This is because it is a three dimensional figure with 3 variables namely r, r (r²) and h.

In a lot of homework sums you will find that you have to convert these cubic inches into gallons. So how to measure the volume in gallons? Simple, one US gallon is 231 cubic inches. So by dividing the result by 231, you get the volume in gallons.

4400 in³/231

19.0476 gallons.

This means that a cylinder which has a radius of 10 inches and a height of 14 inches will hold approximately 19 gallons of a liquid. Like I said, the chapter on mensuration is easy bait and hence, you should try and score as many marks as you can in this chapter.