A cylinder and a cone have equal radii of their bases and equal heights If their curved surface area...

Question

A cylinder and a cone have equal radii of their bases and equal heights If their curved surface areas are in the ratio 85 show that the radius and height of each has the ratio 34

Accepted Answer

ANSWER Consider the curved surface area of cylinder and cone as 8x and 5x So we get 2 rh 8x 1 r h2 r2 5x 2 By squaring equation 1 2 rh 2 8x 2 So we get 4 2r2h2 64 x2 3 By squaring equation 2 2r2 h2 r2 25x2 4 Dividing equation 3 by 4 4 2r2h2 2r2 h2 r2 64 x225x2 On further calculation h2 h2 r2 1625 It can be written as 9 h2 16 r2 So we get r2 h2 916 By taking square root r h We get r h 34 Therefore it is proved that the radius and height of each has the ratio 34

RS Aggarwal Solutions Class 9 Mathematics Solutions for Volume And Surface Area Of Solids Exercise 15C in Chapter 15 - Volume And Surface Area Of Solids