Solution:

Given internal radius of the tube, r = 3 cm

Thickness of the tube = ½ cm = 0.5 cm

External radius of tube = 3+0.5 = 3.5 cm

Height of the tube, h = 21 cm

Volume of the tube = (R²-r²)h

= (3.5²-3²)×21

= (12.25-9)×21

= (3.25)×21

= 68.25 cm³

Height of the cone, h = 7 cm

Let r be radius of cone.

Volume of cone = (1/3)r²h

= (1/3)r²×7

= (7/3)r²

Since tube is melted and changed into a cone, their volumes remain same.

(7/3)r² = 68.25

r² = 68.25×3/7 = 29.25

Taking square root on both sides

r = 5.4 cm

Hence the radius of the cone is 5.4 cm.