Volume of a Cylinder |mathematical lesson

 

In today's class, i will teach you how to calculate a given cylinder of any container of an object. In mathematical definition, it is said to be a prism with a circular cross-section.Hence if we know the area of the circle and the length of height, then we can fine the volume. We all under stand that a cylinder is a solid object/shape with an open area with two parallel line.

This object are in different shape.In real life the arr containers that hold a volume of capacity.We make used of these object daily.Some of these are:

1. Bournvita  container

2. Milo container

3. Pick-Milk container

4.Glass cup

5.canes etc.

As a student, you should always remember the formula given as a key to fine the volume of a cylinder.

Volume of a cylinder = Area of circle and height.

                                      = ㄫr²h

Cylinder = = ㄫr²h

To calculate any given cylinder, you must use the formula.

ㄫ means pie, which the round body of a container.

r² means the radius of a cylinder ( top and the bottom side of a  cylinder)

h means the height of the cylinder 

All the elements listed are called factors of a cylinder.

Now let's solve some examples of a cylinder with area and height( the area is made up of pie and radius).

Example 1:

                                                                                                      1

Find the volume of a cylinder whose base radius is 10-------------------cm

                                                                                                      2

and height 10 cm;

                                             1                                        

Radius of cylinder = 10 -----------

                                              2

                                  

                                         21

Height of cylinder = ----------------

                                          2

Volume of cylinder =  ㄫr²h

       22                 21                   21

------------  x -------------  x --------------- 10

       7                  2                      2

= 3465cm³

Note: A cylinder is one the 3 dimensional shape.It is well clear that a cylinder has three dimensional shapes.also remember, pie is always 22/7 or 3.14.

The first part is the body which is the pie.

The second part is the top and bottom side.

The third part is the height.   

Example 2

Find the total area of a Pepsi cane whose  radius is 3.2cm and height 15cm.

                 22

ㄫ =  ---------------- 

                 7

Volume of  a cylinder =  Area of circle  x  height

                                    = ㄫr²h

 

            22                   4.2    x   4.2              15

=  ---------------   x ---------------------  x -------------

            7                           1                          1                    

  =  831.6

Calculate the volume of  a cylinder whose diameter is 14cm and height 15cm.

                22

ㄫ = ---------------

                 7

  Volume of cylinder =  ㄫd

              22

ㄫ = -------------

               7

    

          22              14 x 14                 15

=-------------- x ---------------- x --------------cm³

          7                    1                        1

 = 9 240cm³

Volume of  a Sphere

A sphere is a round object that has a capacity to hold an air,We can consider a football as an example.Now, i will calculate some exercise,but its also has a formula.Before you can do that,formula must be known.The volume of sphere is given below:

                                        4

Volume of sphere V = ---------ㄫr³

                                        3

Example

                                                                  1      

Fine the volume of a sphere of radius 5---------

                                                                  4

                                       4

Volume of sphere V = ---------ㄫr³

                                        3

                                  1               

Radius of sphere =5--------- 

                                  4

           4           22              21             21              21

  = --------- x --------- x----------- x ---------- x -----------cm²

           3            2               4                4               4

                8

   = 606 -------- cm³

                8

Now solve the following:

(a) Radius 3½ cm, height =10 cm take , ㄫ= 22/7

(b) 10½  cm ,height = 10cm,  = 10cm, ㄫ = 22/7

(c) diameter 12½ cm,height = 17 cm , ㄫ = 22/7

(d) Find the volume of a sphere of:

i. radius = 3cm 

ii. radius = 7cm

iii. diameter = 8cm

iv. diameter = 5cm, take = 22/7

That is how how to fine the volume of a cylinder and sphere.To find the volume, you must remember the of  the mentioned shapes.There are all solid shapes.If ther questions,put them in the comments box.