Radius of base of a hollow cone is 8 cm and its height is 15 cm. A sphere of largest radius is put inside the cone. What is the ratio of the radius of base of cone to the radius of shpere ?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 ie 5 : 3.
Radius of base of cone = 8 cm
Height = 15 cm
AM = 15
Let OM = r [radius of sphere]
In ΔAOD and ΔAMC
∠D = ∠M = 90°
∠A = common
So, ΔAOD ~ ΔAMC
Now, 17/(15 - r) = 8/r ; r = 24/5
Radius of cone/Radius of sphere = (8 × 5)/24
= 5 : 3