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Question
The total surface area of a cylinder is 6512 cm2 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` cm2 (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` cm3 = 36960 cm3
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