A sector of angle 200 degrees is cut from a circle of radius 18cm. the sector is then folded to form a cone,find,correct to two decimal places i.the radius of the cone ii.the height of the cone iii.the vertical angle of the cone iv.the surface area of the cone v.volume of the cone . pi=22/7
Answers
(i) the radius of the cone
The length of the arc of the cone = 200/360 x 2x22/7 x 18
= 62.86
This is equal to the circumference of the base of the cone.
If we take r to be the radius of the cone, then
2x 22/7 x r = 62.86
r = (62.86 x 7)/(2 x 22) = 10.00
(ii) the height of the cone
The slant height of the cone = the radius of the sector
Take height of the cone = h
By Pythagoras theorem
h^2 = 18^2 -10^2
h^2 = 224
h = 14.95
(iii) the vertical angle of the cone
The vertical angle can be divided by 2, so we find one side first, then we multiply by 2
If half vertical angle = x, then
Tan x = 10/14.95 = 0.668
x = 33.75
therefore, vertical angle = 2 x 33.75 = 67.50
(iv) the surface area of the cone
Surface area of cone = pi x r x l (l is the slant height)
22/7 x 10 x 18 = 565.71
It is also equal to the area of the sector = 200/360 x 22/7 x 18^2 = 565.71
(v) volume of the cone .
Volume of cone = 1/3 x base area x height
= 1/3 x 22/7 x 10^2 x 14.95 = 1566.19
