The generatrix of the cone is 13 cm, and its height is 12 cm, find a) the radius of the base of the cone
| August 13, 2021 | education
The generatrix of the cone is 13 cm, and its height is 12 cm, find a) the radius of the base of the cone b) the area of the axial section
The axial section of the cone is an isosceles triangle ABC, the base of which is the diameter of the circle at the base of the cone, and the lateral sides are its generators.
The height BО of the cone is the height of the isosceles triangle, as well as its median and bisector.
Triangle BОC is rectangular, in which, according to the Pythagorean theorem, we determine the length of the leg OC.
OC ^ 2 = R ^ 2 = BC ^ 2 – BO ^ 2 = 169 – 144 = 25.
R = 5 cm.
Then Ssec = ОC * ОВ / 2 = 5 * 12/2 = 30 cm2.
Answer: The axial section area is 30 cm2, the base radius is 5 cm.
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