Surface Area Of Cylinders In Terms Of Pi And 3 14

hey there what we're going to do in this tutorial is we are going to find the surface area of cylinder so basically what we're doing is we're finding the area of these two congruent circles and the area of the rectangular surface wrapped around the side of the cylinder and adding those three surfaces together and that can be represented by the formula 2 pi squared Plus pi times diameter times the height of the cylinder now this part of our formula will give us the area of the two circles and this part of the formula gives us the area of the rectangular side so let's go ahead and get started now what like to do first is don't like to plug 3.14 in for pi even if they ask you to like to solve in terms of Pi first so what I'm going to do is I'm going to rewrite this formula as 2 pi and the radius of our cylinder is four centimeters so we're going to take 4 and square it and then we're going to add it to pi times diameter and remember the diameter is just double the radius so if the radius is 4 the diameter is 8 and then we're going to multiply that by the height of the cylinder which is 10 centimeters all right so let's go ahead and simplify this side of our equation and this side of our equation so we're going to take 4 and square it which is 16 and then we're going to double 16 which is 32. we're going to write 32 multiplied by pi and we're going to add that to 8 times 10 which is 80. so we're going to add that to 80. pi all right now we have two terms in our equation and we just have to combine them because they're like terms so 80 plus 32 is 112. pi square centimeters now if you are asked to solve in terms of Pi we would be finished this would be our answer now if you had to solve using 3.14 for pi all you have to do is plug 3.14 in for pi and multiply it by 112. so let us go ahead and do that really quick so we have 112 we're going to multiply that by 3.14 all right 4 times 112 is 448 all right 1 times 112 of course is 112 and 3 sets of 112 would be 36 all right this column is eight this column is six this column is 11 5 and 3. and of course our decimal point goes right here so if we use 3.14 for pi we end up getting surface area that is approximately equal to 351 and 68 hundredths Square centimeters now the reason said approximately equal to is because 3.14 is an approximation for pi so as soon as you use an approximation in your formula the result itself is an approximation and that is all there is to it this is how you find the surface area of cylinder