Find the volume of the cone to be constructed from a sector having a diameter of 72 cm and a central angle of 210

Question

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Answer 1

the arc length of the sector is s = rθ = 36(210/360)(2π) = 132

That becomes the circumference of the base of the cone.

So, the radius of the base of the cone is 132/(2π) = 21

Now look at the cone from the side. Its height h is given by

21^2 + h^2 = 36^2

Now you have r and h for the cone, so figure its volume the usual way.