Question

A cylinder of radius 4.5 cm and height 12 cm just fits in another cylinder completely with their axis perpendicular. What is the radius (in cm) of second cylinder?

Answer 1

Assume given cylinder placed in horizontal inside of the other cylinder of radius R is placed in vertical .
I saw a rough daigram of given condition, inside second cylinder we see diameter and height of small cylinder are sides of rectangle . Where diameter of second cylinder is diagonal of rectangle.

So, diameter of second cylinder = diagonal of rectangle
= √{9² + 12²}
= √{81 + 144} = √{225}
= 15 cm
Hence, radius = diameter/2 = 15/2 = 7.5 cm

Answer 2

Solution :-

Let us assume that the inner cylinder is placed with its axis horizontal within a cylinder whose axis is vertical.

And, 

Consider a horizontal plane cutting through the center of the inner cylinder. We will have a rectangle of length = 12 cm and width = (4.5*2) = 9 cm

From the center of the inner cylinder find the hypotenuse of the right angled triangle of sides 12/2 = 6 cm and 4.5 cm (which is the radius of the outer cylinder) 

⇒ √[(12/2)² + (4.5)²]

⇒ √(6)² + (4.5)²

⇒ √36 + 20.25

⇒ √56.25

= 7.5 cm

So, radius of the second cylinder is 7.5 cm.

Answer.