Find the curved surface area and the total surface area of the cylinder for which:

(i) h = 16 cm, r = 10.5 cm

(ii) h = 5 cm, r = 21 cm

(iii) h = 20 cm, r = 14 cm

(iv) h = 1 m, r = 1.4 cm

(i) Total surface area of cylinder = 2πr(h + r)

$= 2 \times \dfrac{22}{7} \times 10.5(10.5 + 16) \\[1em] = 2 \times \dfrac{22}{7} \times 10.5(26.5) \\[1em] = 2 \times \dfrac{22}{7} \times 278.25 \\[1em] = 1749 \text{ cm}^2$

Curved surface area of cylinder = 2πrh

$= 2 \times \dfrac{22}{7} \times 10.5 \times 16 \\[1em] = \dfrac{7392}{7} \\[1em] = 1056 \text{ cm}^2$

Hence, the curved surface area = 1056 cm² and the total surface area of the cylinder = 1749 cm².

(ii) Total surface area of cylinder = 2πr(h + r)

$= 2 \times \dfrac{22}{7} \times 21(21 + 5) \\[1em] = 2 \times \dfrac{22}{7} \times 21(26) \\[1em] = \dfrac{24024}{7} \\[1em] = 3432 \text{ cm}^2$

Curved surface area of cylinder = 2πrh

$= 2 \times \dfrac{22}{7} \times 21 \times 5 \\[1em] = \dfrac{4620}{7} \\[1em] = 660 \text{ cm}^2$

Hence, the curved surface area = 660 cm² and the total surface area of the cylinder = 3432 cm².

(iii) Total surface area of cylinder = 2πr(h + r)

$= 2 \times \dfrac{22}{7} \times 14(14 + 20) \\[1em] = 2 \times \dfrac{22}{7} \times 14(34) \\[1em] = \dfrac{20944}{7} \\[1em] = 2992 \text{ cm}^2$

Curved surface area of cylinder = 2πrh

$= 2 \times \dfrac{22}{7} \times 14 \times 20 \\[1em] = \dfrac{12320}{7} \\[1em] = 1760 \text{ cm}^2$

Hence, the curved surface area = 1760 cm² and the total surface area of the cylinder = 2992 cm².

(iv) Given, h = 1 m = 100 cm and r = 1.4 cm

Total surface area of cylinder = 2πr(h + r)

$= 2 \times \dfrac{22}{7} \times 1.4 \times (1.4 + 100) \\[1em] = 2 \times \dfrac{22}{7} \times 1.4 \times (101.4) \\[1em] = \dfrac{6246.24}{7} \\[1em] = 892.32 \text{ cm}^2$

Curved surface area of cylinder = 2πrh

$= 2 \times \dfrac{22}{7} \times 1.4 \times 100 \\[1em] = \dfrac{6160}{7} \\[1em] = 880 \text{ cm}^2$

Hence, the curved surface area = 880 cm² and the total surface area of the cylinder = 892.32 cm².