SOLUTION: A sheet of metal in the form of a sector of a circle of angle 90 degrees and radius 16cm is folded to form an open conical cup. The capacity of the cup is -?

Question 2031: A sheet of metal in the form of a sector of a circle of angle 90 degrees and radius 16cm is folded to form an open conical cup. The capacity of the cup is -?

Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
After folded the top of the cone is a circle which perimeter is equal to
the length of the arc of the sector. It is 16 pi/2 = 8pi cm.
Hence,the radius of the top circle is 8pi/2pi= 4 cm.
------- (the diameter of the top is 8cm)
\ |
\ | h (height of the cone)
\|
Note: the hypotenuse 16^2 = 4^2 + h^2, so h = 4^2(4^2 -1) = 15*4^2,
so, h = 4 sqrt(15)
Hence, the volume of the cone(1/3 area of Base * Height)
= 1/3 pi r^2 h = 1/3 pi 4^2 *4 sqrt(15)
= 64 sqrt(15)/3 cm^3
Kenny
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