Quandaries and Queries


A sphere with radius 5cm is inscribed in a right circular cone 20 cm in height.find
(a) the base radius ,volume of the cone
(b)volume of the shaded space( to 3 sig fig)



I drew a diagram and labeled some points.

Angle ABC is a right angle and since AC is tangent to the circle, angle OPA is also a right angle. Thus triangles AOP and ABC are similar. Now list some facts that you know.

  • |AB| = 20 cm

  • |OB| = |OP| = 5 cm

  • thus |AO| = 15 cm

  • From Pythagoras' theorem AP = sqrt(|AO|2 - |OP|2) = 10 sqrt(2)

  • From the similar triangles |OA|/|AC| = |AP|/|AB| and |OA|/|AC| = |OP|/|BC|

Find |BC|



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