SOLUTION: 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 possibl

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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.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%2F360*pi%2A12%5E2
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%2Ar%2As+=+SA
pi%2Ar%2A12+=+150.8 , find r, the radius of the cone
r = 150.8%2F%2812%2Api%29
r = 4 cm is the radius
find the height of the cone
h = sqrt%28s%5E2-r%5E2%29
h = sqrt%2812%5E2-4%5E2%29
h = 11.3 cm is the height of the cone
Find the capacity (volume)
V+=+1%2F3*+pi%2Ar%5E2%2Ah
V = 1%2F3*pi%2A4%5E2%2A11.3
V = 189.33 cu/cm