Find the volume of the cone if the base radius is 10 dm and the axial section area is 500 dm2.

univerkov | March 16, 2021 | education

Data: R – base radius (R = 10 dm); Sos – the area of the axial section of the taken cone, isosceles triangle (Sos = 500Π dm2).

1) The base of an isosceles triangle: losn = 2R = 2 * 10 = 20 dm.

2) The height of the triangle, cone: Sos = losn * h / 2, from where we express: h = 2Sos / losn = 2 * 500Π / 20 = 50Π.

3) Volume of the cone: Vx = Π * R ^ 2 * h / 3 = Π * 10 ^ 2 * 50Π / 3 ≈ 16432.7 dm3 ≈ 16.4 m3.

Answer: The volume of the cone should be 16.4 m3.

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