The height of the cone is 8, and the length of the generatrix is 10. Find the area of the axial section of this cone.
| August 10, 2021 | education
The axial section ABC of the cone is an isosceles triangle ABC, and of which AC = BC = 10 cm.
The height OC of the cone is the height, the bisector and the median of the triangle ABC, then the height of the OC divides the triangle ABC into two equal triangles, AOC and BOC, which are equal in hypotenuse and leg.
In a right-angled triangle AOC, AO ^ 2 = AC ^ 2 – OC ^ 2 = 100 – 64 = 36.
AO = 6 cm.
Then Saos = AO * OC / 2 = 6 * 8/2 = 24 cm2.
Ssection = 2 * Saos = 2 * 24 = 48 cm2.
Answer: The cross-sectional area is 48 cm2.
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