Solution:

(i) Given diameter of the cylinder, d = 20 cm

Radius, r = d/2 = 20/2 = 10 cm

Curved surface area = 1000 cm²

2rh = 1000

2×3.14×10×h = 1000

62.8h = 1000

h = 1000/62.8

= 15.9 cm

Hence the height of the cylinder is 15.9 cm.

(ii)Volume of the cylinder, V = r²h

= 3.14×10²×15.9

= 4992.6 cm³

Hence the volume of the cylinder is 4992.6 cm³.