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Sum

The total surface area of a cylinder is 6512 cm^{2} and the circumference of its bases is 88 cm. Find:

(i) its radius

(ii) its volume

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#### Solution

Let r be the radius and h be the height of the given cylinder.

Circumference = 2πr = 88 cm (Given)

⇒ `2 xx 22/7 xx r = 88`cm

⇒ `r = 88 xx 7/22 xx 1/2`

⇒ r = 14 cm

Total surface area = `2pir(h + r) = 6512` cm^{2} (Given)

⇒ `88(h + 14) = 6512` (∵ `2pir = 88` cm and r = 14 cm)

⇒ `h + 14 = 6512/88`

⇒ h + 14 = 74 ⇒ h = 60 cm

∴ Volume of the cylinder = `pir^2h`

= `22/7 xx (14)^2 xx 60` cm^{3} = 36960 cm^{3}

Concept: Surface Area of a Cuboid

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