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.)

Logic Jun 8, 2019

#1**+2 **

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

#1**+2 **

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