The radius of the base of the cone is 4√5cm, and the distance from the center of its base
| May 10, 2021 | education
The radius of the base of the cone is 4√5cm, and the distance from the center of its base to the generatrix is 8cm. Find the volume of the cone.
The segment OK is perpendicular to the generator AB, then the triangle AOK is rectangular, then, according to the Pythagorean theorem, AK ^ 2 = AO ^ 2 – OK ^ 2 = (4 * √5) ^ 2 – 8 ^ 2 = 80 – 64 = 16.
AK = 4 cm.
The right-angled triangles AOK and BOK are similar in acute angle, then:
ОВ / ОА = OK / AK.
ОВ = ОА * OK / AK = 4 * √5 * 8/4 = 8 * √5 cm.
Determine the volume of the cone.
V = Ssc * h / 3 = π * OA ^ 2 * OB / 3 = π * (4 * √5) ^ 2 * 8 * √5 / 3 = π * 80 * 8 * √5 / 3 = π * 640 * √5 / 3 cm3.
Answer: The volume of the cone is π * 640 * √5 / 3 cm3.
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