Mathematics

A cylinder has a diameter of 20 cm. The area of curved surface is 100 cm². Find :
(i) the height of the cylinder correct to one decimal place.
(ii) the volume of the cylinder correct to one decimal place.

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Given,

The diameter of the cylinder = 20 cm

So, the radius (r) = $\dfrac{20}{2}$ = 10 cm

Given, the curved surface area = 100 cm².

Let height = h cm

(i) By formula,

Curved surface area of cylinder = 2πrh

∴ 2πrh = 100

⇒ 2 x $\dfrac{22}{7}$ x 10 x h = 100

⇒ h = $\dfrac{100 \times 7}{22 \times 10 \times 2}$

⇒ h = $\dfrac{700}{440}$ = 1.6 cm.

Hence, the height of cylinder = 1.6 cm.

(ii) By formula,

Volume of the cylinder = πr²h

= $\dfrac{22}{7}$ x 10 x 10 x 1.6

= 502.9 cm³.

Hence, the volume of cylinder = 502.9 cm³.

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