# math

A sector of a circle subtending an angle 300 degrees at the centre is used to form a cone with base radius 6cm. Find the (a.)radius of the circle (b.)volume of the cone (c.)area of the minor sector of the circle

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1. It often helps to see a physical model of the problem
Cut out a circular sector with scissors and form it into a cone.
You will see that the arc length of the sector becomes the circumference of the circular base of the cone

if the cone is to have a radius of 6 cm, then its circumference is 12π cm

You should be familiar with the relation,
arc = rØ for a sector, where Ø is the sector angle in radians
300° to radians --->Ø/2π = 300/360---> Ø = 10π/6

12π = r(10π/6)
r = 12π(6/10π) = 7.2
So our sector must have a radius of 7.2 cm

b) If you look at your model you will see that 72 cm becomes the "slant" length of the cone, so using Pythagoras,
h^2 + 6^2 = 7.2^2 , where h is the height of the cone
h = √15.84

volume = (1/3) base x height
= (1/3)(36π)(√15.84)
= appr 150.04 cm^3

c) area of minor sector....
our needed sector is 5/6 of the circle, so the minor sector would be 1/6 of the area of the circle

area of minor sector = (1/6)π(7.2^2)
= appr 27.14 cm^2

check my arithmetic.

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