Question

A sector of a circle of radius 7.2cm subtends an angle of 300° at the centre. It is used to form a cone . Calculate the vertical angle of the cone to the nearest degree

Answer 1

Answer:

112.89 °

Step-by-step explanation:

Arc length of sector = θ/360 pi d

300/360 *3.142*2(7.2)

=37.704c

This arc length forms the circumference

Slant height = radius of circle =7.2 cm

Circumference =2 pi r

37.704=2*3.142r

37.704=6.284r

r=37.704/6.284

r= 6cm

Triangle formed where r =opposite and l= hypotenuse

Sin θ=Opp/hyp

Sin θ=6/7.2

Sin θ=0.8333

θ=sin^-1 0.8333

θ=56.44

Angle gotten is θ

And the angle required is twice that gotten from the triangle =2θ

=2*56.44=112.89 degrees

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