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प्रश्न
The radius of the base and the height of a solid right circular cylinder are in the ratio 2 : 3 and its volume is 1617 cm3. Find the total surface area of the cylinder.
उत्तर
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=(1617+7/22xx12)`
`=> 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:
(2πrh + 2πr2)
= 2πr(h + r)
`= 2xx22/7xx7xx(21/2+7)"cm"^`
`= (2xx(22)/7xx7xx(35)/2) "cm"^2 `
= 770 cm2
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