Solution:

Given height of the cylinder, h = 9 cm

Diameter of the cylinder = 40 cm

Radius of the cylinder, r = 40/2= 20 cm

Volume of the cylinder = r²h

= ×20²×9

= ×400×9

= 3600 cm³

Height of the cone, H = 108 cm

Volume of cone = (1/3)r²h

= (1/3)r²×108

= 36r²

Since volume of cone is equal to the volume of the cylinder, we get

36r² = 3600

r² = 3600/36

r² = 100

Taking square root on both sides,

r = 10 cm

Hence the radius of the cone is 10 cm.