Question:What is Circle? 

A circle is the path traces out by point which moves in a plane so that it is always the same distance from a fixed point in that plane.
The fixed point is called the center of the circle and the distance of the point from the center of the circle is called the radius.
If the point could move anywhere in space and where not obliged to lie in a plane, it would trace out a sphere.

Question:Define diameter, chord, circumference, arc. 

Diameter: A diameter of a circle is a line through its center terminated at  each end by the circumference of the circle.  chord: A chord of a circle is a line joining any two points  on the circle.circumference: The circumference of a circle is the distance round the circle .Arc: An arc of a circle is a circle is part of the circumference. A major arc is an arc greater then half the circumference. A minor arc is an arc less than half the circumference.

Question:Find the circumference of a circle of radius  5 cm. 

C = 2`pi` r=2`pi xx`5 cm=10`pi`cm
                                        =31.42 cm
                                        =31.4 cm  (to 3 sig. fig)

Question:Taking `pi` to be `22/7`, find the radius of a circle whose circumference is 44 cm. 

C = 2`pi`r 

`:.` r = `C/(2pi)`

         = `44/(2 xx 22/7)`

         = 7.

The radius of the circle is 7 cm.

Question:Find the area of a circle of radius 7 cm. Take `pi` to be `22/7` . 

A = `pi r^2`

   = `22/7 xx (7)^2 cm^2`

   = 22 `xx 7 cm^2`

   = 154 `cm^2`

Question:Find the radios of a circle of area 38.5 `cm^2`  (`pi =22/7` ). 

`pi r^2` = 38.5

`:. r^2` = `38.5/pi` 

         = `(38.5 xx 7)/22`

         = `(3.5 xx 7)/2`

         = `(3.5)^2` .

   `:.`r = 3.5

The radius of the circle is 3.5 cm

Question:Find the area between two circles of radii 4 cm and 3 cm . given that the smaller circle lies entirely within the larger. 

Area of the bigger circle =`pi(4)^2 cm^2` =16`pi cm^2`.

Area of the smaller circle=`pi(3)^2``cm^2`= 9`pi cm^2` .

Area between the circle = (16`pi`- 9`pi`) `cm^2`= 7`pi cm^2`.

                                      = 7`xx 22/7 cm^2`

                                      = 22 `cm^2`

Question:Find  the volume and total surface  area of a right  circular cylinder , the radius of whose base  is 4 cm and whose height is 5 cm  ( Take `pi` to be 3.142) . 

The volume =`pi r^2`h=`pi(4)^2 5 cm^3`

                   = 80`pi cm^3`.

                   = 251.36 `cm^3`

                   = 251 `cm^3`

 The area of the curved  surface = 2`pi`rh

                                 = 2`pi`(4)(5) `cm^2`  

                                 = 40`pi cm^2`.

The area of each end = `pir^2`=`pi(4)^2 cm^2` = 16`pi cm^2`.

The total surface area =(40`pi`+32`pi`) `cm^2`

                                   = 72`pi cm^2`

                                   =226.224 `cm^2`

                                   226 `cm^2`

Question:Find the volume of material in pipe of length 7 cm, if the internal and external radii are 3 cm and 4 cm (Take `pi` to be `22/7`). 

The volume of the larger cylinder

                   = `pi(4)^2` 7 c`m^3`= `pi xx16 xx 7 cm^3`= 112`pi cm^3`.

The volume of the smaller cylinder

                   = `pi(3)^2` 7 c`m^3`= 63`pi cm^3`

The volume of the material
                   = (`112 pi - 63 pi` ) `cm^3`

                   = 49`pi cm^3`

                   = 49`xx 22/7 cm^3`.

                   = 154 `cm^3`.