Find the radius of the cone if its height is 2 cm, and the generatrix is 9 cm.
July 27, 2021 | education|
In order to obtain a cone, it is necessary to turn a right-angled triangle around one of its legs.
This triangle, in this case, will be half the axial section of this cone. For convenience, we will designate it as ABC, where:
AB – Generating, the length of which is 9 cm;
ВС – height, the length of which is 2 cm;
AC is the radius of the base.
Since the triangle is rectangular, we apply the Pythagorean theorem:
AB ^ 2 = BC ^ 2 + AC ^ 2;
AC ^ 2 = AB ^ 2 – BC ^ 2;
AC ^ 2 = 92 – 22 = 81 – 4 = 77;
AC = √77 = 8.8 cm.
Answer: The radius of the base of the cone is 8.8 cm.
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