DC = 8 cm ∴ BC = √(6)2+(8)2 = √36+64 = 10 cm In ΔACD and ΔEOC ∠ADC =∠OEC = 90° ∠ACD = ∠OCE (common angle) ∠CAD = ∠EOC (remaining angle) ∴ ΔACD ~ ΔEOC Also, AD = AE = 6 cm (∵ the length of two tangents drawn from an external point to circle are equal) ∴ EC = AC - AE = 10 - 6 = 4 cm In similar ΔACD and ΔEOC
DC
AD
=
EC
OE
⇒ OE=
AD×EC
DC
=
6x4
8
= 3 cm ∴ Required of sphere = 3 cm Now, volume of cone =