Math CentralQuandaries & Queries


Question from elwin, a student:

i have a sector of a circle that has 120 degree and 6 cm length. What will be the diameter of the base of the cone.
and what is the diameter of the angle is changed to 180.
thx in advance for your help :)

Hi Elwin,

Look at the first two diagrams in my response to a question from Steve a few years ago. You have the length $a$ of the arc to be 6 cm. When the sector is rolled up to form a cone this arc is the circumference of the circular base. The circumference of a circle is $\pi \times d$ where $d$ is the diameter. What is the diameter when the circumference is 6 cm?


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