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A section is cut out of a circular piece of paper having radius four inches, as shown. Points A and B are then glued together to form a right circular cone. What is the circumference of the base of the resulting cone? Express your answer in terms of \(\pi\). (The \(270^\circ\) sector forms the cone.)

 Jun 8, 2019
edited by Logic  Jun 8, 2019

Best Answer 

 #1
avatar+8756 
+3

circumference of base of cone  =  length of major arc AB

 

length of major arc AB  =  \(\frac{270}{360}\cdot\) circumference of circle

 

length of major arc AB  =  \(\frac{270}{360}\cdot2\pi\cdot4"\)

 

length of major arc AB  =  \(\frac{3}{4}\cdot2\pi\cdot4"\)

 

length of major arc AB  =  \(6\pi"\)_

 Jun 8, 2019
 #1
avatar+8756 
+3
Best Answer

circumference of base of cone  =  length of major arc AB

 

length of major arc AB  =  \(\frac{270}{360}\cdot\) circumference of circle

 

length of major arc AB  =  \(\frac{270}{360}\cdot2\pi\cdot4"\)

 

length of major arc AB  =  \(\frac{3}{4}\cdot2\pi\cdot4"\)

 

length of major arc AB  =  \(6\pi"\)_

hectictar Jun 8, 2019
 #2
avatar+1229 
+2

Thank You Hectictar!

Logic  Jun 8, 2019

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