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Question
The ratio between the radius of the base and the height of a cylinder is 2 : 3. If its volume is 1617 cm3, the total surface area of the cylinder is
Options
308 cm2
462 cm2
540 cm2
770 cm2
Solution
770 cm2
Let the common multiple be x.
Let the radius of the cylinder be 2x cm and its height be 3x cm.
Then, volume of the cylinder `= pi"r"^2"h"`
`= 22/7xx(2x)^2xx3x`
Therefore,
`22/7xx(2x)^2xx3x=1617`
`=> 22/7xx4x^2xx3x = 1617`
`=>22/7xx12x^3=1617`
`=x^3 = (1617xx7/22xx1/12)`
`= x^3 = (7/2xx7/2xx7/2)`
`=x^3 = (7/2)^3`
`=> x= 7/2`
Now, r = 7 cm and `"h" = 21/2 "cm"`
Hence, the total surface area of the cylinder
`=(2pi"rh"+2pi"r"^2)`
`= 2pi"r"(2xx22/7xx7xx35/2)"cm"^2`
= 770 cm2
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