A sector of a circle of radius 12cm has the angle 120o. It is rolled up so that two bounding radii are joined to form a cone. Find the volume of the cone.

When a sector of a circle is rolled up in a given manner, we obtain a cone whose slant height is equal to the radius of the sector and the circumference if the base of the cone is equal to the length of the are of sector.

Now length of the acc of the sector  square u

Let rein be the radius of the base, h cm be the height and l cm be the slant height of the cone. Then, 
l = radius of the sector
= 12 cm.

Circumference of the base of the cone = Length of the arc of the sector 
  

Now l2 = r2 + h2


.

Let V cm3 be the volume of the cone. Then, 
 cubic unit.

Taking log on both sides logV
log22 + log128 + log2 - log21 


logV = 2.2779
V = anti log (2.2779)
= 189.5
Hence the volume of the cone is 189.5 cm3.

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logarithms in 10th!!! you've got to be kiddin me!!

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 l=theeta/180*pieR

=120/180*PIE *12

L=8 PIE

CI9RCUMFRENCE OF BASE OF CONE =2PIE R

8PIE=2PIE R

R=4

FIND H AND THE SOLVE

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hahahah....no one has said that * NOT TO USE LOGARITHMS* so i think its fine... does it matter??

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Angle of the sector = 120Radius of the sector = 12 cm.Length of the arc of the sector = 2r= 2x 12= 8cmLet r be the radius of the cone formed after folding and joining the two radii. The circumference of the base of the cone is equal to the arc of the sector.2r = 8r = 4 cmThus, the radius of the cone = 4 cmlet h be the height of the conel2= r2+ h2h ==h2 == 128h == 8cmVolume of cone =r2h=x 4 x 4 x 8 = = 189.639 cm3

  • -3
When the sector is cut from the circle it will have a curved length of one third of the circle. This will be πd/3 where d is the 24 cm diameter of the circle. This yields: 

π(24)/3 = 8π 

When the cone is rolled it will then have a circular base with this 8π circumference. The cone will also have a side length of 12 cm, which is important to find the height of the cone. First we need to find the radius of the base of the cone. We know that the circular base has a circumference of 8π and : 

c=πd So we get: 

8π=πd 

d=8 and r=4 <--- Radius of the circular base. 

For the height use the Pythagorean theorem: 

r2+(height)2=(side )2

42+(height)2=122

h^2=144-16 

h2=128 

h=8√2 

Thus the formula for the volume of a cone: 

V=1/3bh Where b is the area of the base. 

V=1/3π(4)2(8√2) 

V=1/3π128√2 <----- Answer 

V=189.56 <----- Approximate answer 
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Thanx for every one
  • -3
came to  know what is logarithims only now.
thx for using it.
cheers
  • -4
Sorry for my poor handwriting. :)

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sector of a circle of radius 12 cm has the angle 120 degree. it is rolled up so that two bounding radii are joined together to form a cone. find the volume of the cone.
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189.56 cubic centimeter is the approximate answer. Refer to the picture for steps.

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