Through two generatrices of the cone, the angle between which is equal to 30 degrees, a section
| August 2, 2021 | education
Through two generatrices of the cone, the angle between which is equal to 30 degrees, a section is drawn with an area of 25 dm2. Find the volume of the cone if the base radius is 8 dm.
The section of the cone is an equilateral triangle CDK, in which CK = DK and at the vertex K is 30.
The area of the triangle СDК is equal to: Sсдк = CК * DК * Sin30 / 2 = CK ^ 2 * Sin30 / 2 = 25 cm2.
SK2 = 2 * Sdk / Sin30 = 2 * 25 / (1/2) = 100.
SK = DK = 10 cm.
In a right-angled triangle KOS, KO ^ 2 = KS ^ 2 – OC ^ 2 = 100 – 64 = 36.
KO = 6 cm.
Determine the area of the base of the cone. Sop = n * R ^ 2 = n * 64 cm2.
The volume of the cone is: V = Sax * OK / 3 = n * 64 * 6/3 = 128 * n cm3.
Answer: The volume of the cone is 128 * n cm3.
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