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

September 15, 2021 | education

| 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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