SOLUTION: The circular sector highlighted has a radius of 6 cm and transforms itself into the lateral surface of a cone after gluing both dotted lines together as represented below: https:

Algebra ->  Volume -> SOLUTION: The circular sector highlighted has a radius of 6 cm and transforms itself into the lateral surface of a cone after gluing both dotted lines together as represented below: https:      Log On


   

Question 1196414: The circular sector highlighted has a radius of 6 cm and transforms itself into the lateral surface of a cone after gluing both dotted lines together as represented below:
https://i.imgur.com/S0yDQc2.png
a. What is the radius of the cone's base (in cm)
b. What is the volume of a cone using the lateral surface and base described above?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


For simplicity I will leave off the units in my discussion.

The circular sector is 5/6 of the whole circle. The length of the curved part of the sector is 5/6 of the circumference of a circle with radius 6: %285%2F6%29%282pi%29%286%29=10pi

That curved part of the sector becomes the circumference of the base of the cone. The radius of the cone is the circumference of its base, divided by 2pi: %2810pi%29%2F%282pi%29=5

ANSWER a. The radius of the base of the cone is 5

The slant height of the cone is the radius of the sector: 6.

The radius of the base of the cone is 5; the slant height is 6; the Pythagorean Theorem tells us the height of the cone is sqrt%2811%29.

The volume of the cone is one-third the area of the base, times the height:

V=%281%2F3%29%28%28pi%29%285%5E2%29%29%28sqrt%2811%29%29

ANSWER b. The volume of the cone is %28%2825%2F3%29sqrt%2811%29%29pi