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 cmQuestion: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`.