FOR GMS ICSE 2014 30th Aug

Dear Students, we shall be starting Ch.22 : Cone and Sphere (Surface  Area and Volume) today.

Mr.O.P.Sharma has already commenced the previous chapter, 21 : Circumference & Area of a circle with you and we need to use the information from there to proceed, so, please remember :

• the circumference (ring) of a circle is 2 x π  x radius
• the area of a circle is π  x radius x radius
• we use the π which is the Greek letter noting the constant ratio between the circumference of a circle and the diameter of a circle.
• please make sure that you have done Ch.21, ex.21 (A) as required by Mr.Sharma, before you proceed onto this matter

Today, we will work with a cylinder. Do you want to know what a cylinder is ? Take any sheet of paper and roll it. What you will get is a circular object of some length (determined by the length of the paper you have rolled). Please look at page 322 of your book to see what a cylinder looks at.

Today, we shall be working at a cylinder without taking into account the thickness of the material which makes up the cylinder (we shall do that tomorrow).

We shall first look at the surface area of a cylinder : there are two conditions for surface area

• an open ended cylinder
• a closed cylinder

An open ended cylinder has neither a lid nor a base. If we cut open this cylinder along its length we will get a rectangle. The breadth of the cylinder will be the circumference of the cylinder. Thus area of the surface of an open cylinder will be 2πr x height of the cylinder. Thus surface area of an open cylinder is 2πrh.

To find the surface area of a closed cylinder we will need to add the areas of the lid and the base. Thus to 2πrh we need to add 2πrr. Thus if we add both we get the surface area of a closed cylinder to be 2πr(h + r)

Now the last things is to find the volume of a cylinder. To do this we first need to understand the idea of a cross-section. the circular face of a cylinder will be the cross-section of the cylinder as the same area goes through the whole length of the cylinder. We will need this term later - so remember it. Thus the volume of the cylinder - a solid cylinder (presuming there is no empty space within) is the area of the circle into the length of the cylinder. this is πrrh (please excuse me - I do not know how to write r-squared in this programme !)

Now, can you attempt : Ex.22(A) : Nos 1 to 12 !

Remember, if you need any help I am just an e-mail away !