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A drill bit, to dig massive holes in the earth, is designed in the shape of a cone so that it is easier to dig farther into the earth. The slant height of the bit measures 5.2 meters and the diameter of the base measures 3.8 meters. If you were to drill just until the cone was level to the ground, how much earth would be displaced?

 Jan 23, 2019
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The radius of the cone is   3.8 / 2  =  1.9 m

 

The height of the cone  =  sqrt [5.2^2 - 1.9^2 ]  = sqrt  [ 27.04 - 3.61]   = sqrt [23.43] m

 

The volume is

 

(1/3)pi * radius^2 * height =

 

(1/3)pi * (1.9)^2 * sqrt (23.43)  ≈    18.3 m^3

 

 

cool cool cool

 Jan 23, 2019

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