The generatrix of the cone, its height and base radius form a right-angled triangle, for which we can write:
L ^ 2 = H ^ 2 + R ^ 2, where L is the generator, H is the height, R is the radius of the base.
By the condition of the problem, the length of the generatrix and the height are known, we find the radius of the base:
R ^ 2 = L ^ 2 – H ^ 2 = 10 ^ 2 – 8 ^ 2 = 100 – 64 = 36 = 62;
R = 6 cm.
The volume of the cone is equal to one third of the product of its height and the area of the base:
V = Ssc * H / 3.
Sop = n * R ^ 2 = n * 6 ^ 2 = 36n cm2.
Find the volume of the cone:
V = 36п * 8/3 = 96p ≈ 301.6 cm3.
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