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A circle of radius 12 is cut out of a piece of paper. A 90 degree sector is then cut from this circle.  This 90 degree sector is rolled into a cone.  What is the volume of the cone?

 Jul 4, 2020
 #1
avatar+21853 
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The circumference of the original circle is:  2·pi·12  =  24pi

 

Since a 90o sector is cut out, one-fourth of the circle is cut out, leaving three-fourths.

Three-fourths of  24pi  =  (3/4)·24pi  =  18 pi.

 

Therefore 18pi is the circumference of the cone.

Finding the radius of the cone:  18pi  =  2·pi·r     --->     r  =  9

 

The radius of the original circle is now the slant height of the cone.

To find the height of the cone, use the right triangle whose hypotenuse is 12 and whose base is 9.

This gives a height of:  h2 + 92  =  122     --->     h = sqrt(63)

 

Volume of a cone:  (1/3)·pi·r2·h     --->     (1/3)·pi·92·sqrt(63)     --->     ....     

 Jul 4, 2020
 #2
avatar+1055 
+1

Hi, Geno! Please take the time and read the question again. smiley

 

A circle of radius 12 is cut out of a piece of paper. A 90-degree sector is then cut from this circle. This 90-degree sector is rolled into a cone. What is the volume of the cone?

 

r = 3        h = 11.619

 

V = pi * r2 * h / 3 ≈ 109.51 u3  smiley

Dragan  Jul 5, 2020
edited by Dragan  Jul 5, 2020
edited by Dragan  Jul 15, 2020

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