The ABC triangle rotates around the larger side a = 13 cm b = 14 cm c = 15 cm Find the volume.

| July 3, 2021 | education

The figure of rotation of the triangle is a double cone with a radius of OA and heights of OB and OC.

By Heron’s theorem, we determine the area of ​​the triangle ABC.

The half-perimeter of the triangle is: p = (13 + 14 + 15) / 2 = 21 cm.

Then Sас = √21 * (21 – 13) * (21 – 14) * (21 – 15) = √7056 = 84 cm2.

Also Savs = BC * AO / 2.

AO = 2 * Savs / BC = 2 * 84/15 = 11.2 cm.

In a right-angled triangle ABO, according to the Pythagorean theorem, OB ^ 2 = AB ^ 2 = AO ^ 2 = 169 – 125.44 = 43.56.

ОВ = 6.6 cm, then OC = ВС – ОВ = 15 – 6.6 = 8.4 cm.

The volume of the ABD cone is: V1 = π * AO ^ 2 * OB / 3 = π * 125.44 * 6.6 / 3 = π * 275.968 cm3.

The volume of the ACD cone is: V2 = π * AO ^ 2 * OC / 3 = π * 125.44 * 8.4 / 3 = π * 351.232 cm3.

V = V1 + V2 = π * 627.2 cm3.

Answer: The volume of the figure is π * 627.2 cm3.



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