Question 1123339
A piece of paper is in the shape of a sector of a circle whose radius is 12 cm and the central angle of the sector is 120 degree.
 It is rolled to form a cone of the biggest possible capacity.
Find the capacity of cone.
:
Find the total area of the sector
A = {{{120/360}}}*{{{pi*12^2}}}
A = 150.8 sq/cm, this is surface area of the cone
:
Surface area (SA) of a cone without the end formula
The slant length (s) = the radius of the paper; 12 cm
{{{pi*r*s = SA}}}
{{{pi*r*12 = 150.8}}} , find r, the radius of the cone
r = {{{150.8/(12*pi)}}}
r = 4 cm is the radius
find the height of the cone
h = {{{sqrt(s^2-r^2)}}}
h = {{{sqrt(12^2-4^2)}}}
h = 11.3 cm is the height of the cone
Find the capacity (volume)
{{{V = 1/3}}}*{{{ pi*r^2*h}}}
V = {{{1/3}}}*{{{pi*4^2*11.3}}}
V = 189.33 cu/cm