# The generatrix of the cone is 10 cm. Find the volume if its height is 8 cm.

July 22, 2021 | education

| 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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