SOLUTION: A sector of 120 degrees has a radius of 9 cm. The sector is then folded to form a cone. Find the exact value for the height "h" of the cone. Hence, find the volume.

Question 1109048: A sector of 120 degrees has a radius of 9 cm. The sector is then folded to form a cone. Find the exact value for the height "h" of the cone. Hence, find the volume.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

The sector is of the circle,
so its arc is of the circumference of radius .
When the sector is folded, that arc will be
the circumference of the base of the cone,
so that circumference will be of the circumference of radius ,
and its radius will be of ,
or .
The slant height of the cone formed is the radius of the sector.
A cross section of the cone passing through apex and center of the base will look like this
As per Pythagorean theorem, the exact value of the height is

.
An approximate value is
Then, the volume is

.
That is the exact expression for the volume.
is an approximate value.
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