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# My question

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Here is my question

Oct 12, 2018

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The slant height of the cone is = BC

The volume of the cone is given by

432pi  = pi/3 * r^2 * height

432pi  = pi / 3 * 12^2  * height

432  = 144/3 * height      multiply both sides by 3/144

3 * 432  / 144  = height

9 cm  = height

Now...the slant height of the cone  = √ [ r^2 +  h^2 ] = √[12^2 + 9^2] =√225  =15 cm = BC

So...the lateral surface area of the cone = the shaded area of the circle  =

pi * radius * slant height  =     pi * 12 * 15  =   180 pi  cm^2

And we can set up the following relationship

Total circumference of the circle / Total area of the circle =

[2*pi * BC] /[ pi * BC^2]  =  [2pi *  BC * ( D /360)]  / [ 180pi ]

Where D is the number of degrees in the arc of the shaded sector

[2 * pi * 15]  /[ pi * 15^2 ] =[ 2 * pi * 15] * ( D / 360)] /[180pi]

1 / 15^2  =   (D / 360) / 180

1 / 15^2  = D / 64800

64800 / 225  = D = 288°

So...the number of degrees in ABC  = 360  - 288   =  72°

Oct 12, 2018
edited by CPhill  Oct 13, 2018
edited by CPhill  Oct 13, 2018