 Let us say we have this ball which looks like a jumping ball we usually used to play in the childhood I think many of us can remember such a ball. I have somehow drawn the grip of a cricket ball on it But let's forget about it This is kind of a jumping ball And if I was interested in finding out how much paint I would need in order to paint that I would need surface area of The ball and ball is a spherical object. So I can say surface area of a sphere How do we get the surface area of the sphere surface area of the sphere? Let us call it s is given as 4 pi r squared Where this r is basically the radius of this ball this area is Equal to the area of the four circles with radius r. So it's four times pi r squared We only need to know our in order to get the surface area We will calculate the area if let's say the radius of this ball was say five centimeters Let's look at intuitively why the surface area of a sphere is four pi r squared So this is a schematic diagram of a sphere of radius r. We can draw a cylinder of height 2r Which exactly is of the height of the sphere as well upper tape of the sphere touches the upper surface of the cylinder and this bottom surface of the sphere touches the bottom Surface of the cylinder it's out of the scope of this video to prove Why surface area of the sphere is equal to surface area of the cylinder like that? But we can approximate the surface area of the sphere With the surface area of the cylinder which encloses the sphere completely and if we open this particular Cylinder what we get is a rectangle like this if we cut that cylinder and just open it up this height will be 2r and The length here inside is going to be this length here will be The circumference of top or bottom surface which is basically 2 pi r because the radius of the sphere is r and the area of this particular rectangle is of course 2r times 2 pi r which is 4 pi r squared and that is how we can visualize that the area of a sphere of radius r Is 4 pi r squared Let's try and solve a problem now So let us calculate the surface area of this ball with radius 5 centimeters the surface area will be s is equal to 4 times we can use the value 22 by 7 for pi r square which is square of 5 centimeters and This is equal to 88 times 25 divided by 7 Centimeter square and if we simplify this we find that the surface area of this ball is Let me just quickly use the calculator. It will be 88 times 25, which is 2200 divided by 7 centimeter square, which is nothing but 314.28 Centimeter square remember that the unit of the surface area here is centimeter square because the unit of the Radius is in centimeters. Usually people ask problems which are dependent upon the surface area For example, if 2 ml of paint is required per centimeter square How much paint is required to paint the the ball and in such case after finding out the total area or the Total surface area we can find a total paint required by Multiplying the total surface area that we have in centimeter square times 2 ml per centimeter square Which gives us 628.57 ml So 628.57 ml of paint will be required to paint the ball completely I will encourage you to find out instances in real life where you will need to find out the surface area of spheres