The height of the cone is 12 and the length of the generatrix is 15. Find the diameter of the base of the cone.

The radius of the base of the cone, its height and the generatrix are related by the ratio: R ^ 2 + H ^ 2 = L ^ 2, where R is the radius of the base of the cone, H is the height of the cone, and L is the length of the generatrix. In our case, we get the equation: R ^ 2 + 12 ^ 2 = 15 ^ 2

R ^ 2 = 15 ^ 2 – 12 ^ 2

R ^ 2 = 225 – 144

R ^ 2 = 81

R = 9

Therefore, the diameter of the base of the cone can be found by the formula: D = 2R

D = 2 * 9 = 18

Answer: D = 18




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