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Question
A rectangular sheet of dimensions 25 cm × 7 cm is rotated about its longer side. Find the volume and the whole surface area of the solid thus generated.
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Solution
A rectangular sheet of dimensions 25 cm × 7 cm is rotated about its longer side which make a cylinder with base 25 cm and height 7 cm.
Surface area of a base = 2πr
∴ 2πr = 25 cm
⇒ `r = (25 xx 7)/(2 xx 22) = 175/44 cm`
Volume of a cylinder = πr2h
= `22/7 xx 175/44 xx 175/44 xx 7`
= `(175 xx 175)/(2 xx 44)`
= `30625/88`
= 348.011 cm3
Surface area = 2πrh
= `2 xx 22/7 xx 175/44 xx 7`
= `44/44 xx 175`
= 175 cm2
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