Quandaries
and Queries
Question:
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)
Hi,
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|
Penny