This week, I have learned how to find the SA (Surface area) of a Cylinder and a Cone. It requires to remember formula and practice to put numbers in the formula.

SA of Cylinder and Pyramid

Before we start to calculate to find the SA, we need to learn the formula.  If you remember a wrong formula, not only you will end up having a wrong answer, but also wasting all calculations.  Let’s carefully go over the formula.

Formula

SA Cylinder: 2π + 2πrh

SA Cone: π + πrs

R= Radius

H= Height

S= Slant height

Now we know the formula for the SA for Cylinder and Cone, we can start to calculate.

 

For above Cylinder, let’s replace the number in the formula: r=1 and h=2.

SA Cylinder: 2π + 2πrh

SA Cylinder:2π + 2π(1)(2)

SA Cylinder: 2π(1) + 2π(2)

SA Cylinder: 6.28 + 12.57

SA Cylinder: 18.85

This is how we can find the answer for the SA of a Cylinder. However when you have the diameter (D) instead of a radius (R), you must divide the diameter by 2 to find the radius.

D= 2R

R= D/2

To find the the SA of a Cone, it will be much harder since we need to find the slant height. To find the slant height, you must use the pythagorean theorem. 

=

Here, we have the radius and the height. We can find the slant height with these 2 numbers. The first, we know that is always the hypotenuse (the longer side of a right triangle).

We can say:

Slant height = =

Slant height = 16 + 196=

Slant height = 212 = 

Slant height =

Slant height = 14.56

As we have the slant height, now we can  calculate the SA of a Cone.

SA Cone: π + πrs

SA Cone: π + π(4)(14.56)

SA Cone: π(8) + π(58.24)

SA Cone: 25.13 + 182.97

SA Cone: 208.1

This was hard at the beginning, but with practice, I believe you can be a master of calculating the SA of a Cylinder and a Cone.