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Question
A solid iron cylinder has total surface area of 1848 sq.m. Its curved surface area is five – sixth of its total surface area. Find the radius and height of the iron cylinder.
Solution
T.S.A of the cylinder = 1848 sq.cm
2πr (h + r) = 1848 ...(1)
Curved surface area = `5/6` × 1848 sq.cm
2πrh = 5 × 308
2πrh = 1540 sq.m ...(2)
Substitute the value of 2πrh in (1)
2πr (h + r) = 1848
2πrh + 2πr2 = 1848
1540 + 2πr2 = 1848
2πr2 = 1848 – 1540
`2 xx 22/7 xx "r"^2` = 308
r2 = `(308 xx 7)/(2 xx 22)` = 49
r = 7
Radius of the cylinder = 7m
2πrh = 1540
`2 xx 22/7 xx 7 xx "h"` = 1540
h = `1540/(2 xx 22)` = 35 m
Radius of the cylinder = 7 m
Height of the cylinder = 35 m
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