A cylinder has a diameter of 20 cm. The area of curved surface is 1000 cm². Find

(i) the height of the cylinder correct to one decimal place.

(ii) the volume of the cylinder correct to one decimal place. (Take π = 3.14)

(i) Radius = $\dfrac{\text{Diameter}}{2} = \dfrac{20}{2}$ = 10 cm.

Curved surface area of cylinder = 2πrh.

Given, curved surface area of cylinder = 1000 cm².

∴ 2πrh = 1000

$\Rightarrow 2 \times \dfrac{22}{7} \times 10 \times h = 1000 \\[1em] \Rightarrow h = \dfrac{1000 \times 7}{2 \times 22 \times 10} \\[1em] \Rightarrow h = \dfrac{7000}{440} \\[1em] \Rightarrow h = 15.9 \text{ cm}.$

Hence, the height of the cylinder = 15.9 cm.

(ii) Volume of cylinder = πr²h.

Putting values we get,

$\text{Volume of cylinder } = 3.14 \times (10)^2 \times 15.9 \\[1em] = 3.14 \times 100 \times 15.9 \\[1em] = 4992.6 \text{ cm}^3.$

Hence, the volume of the cylinder = 4992.6 cm³.