a solid cylinder has a total surface area of 231 sq..., Area & Volume, General Mathematics

Question:A solid cylinder has a total surface area of `231` sq. cm. If its curved surface area is two third of the total surface area, the volume of the cylinder is :

A `269.5 cm^3` 
B `385 cm^3` 
C `308 cm^3` 
D `363.4 cm^3`

/113

+ AnswerA

+ ExplanationCurved Surface Area 

`= (2/3 xx 231) cm^2 = 154 cm^2.`

`:. 2πrh + 2πr^2`

`= 231 ⇒ 154 + 2π r^2`

`= 231`

`:. r^2 = (77 xx 1/2 xx 7/22)`

`= 49/4 or r = 7/2.`

Now,`2πrh`

`= 154 ⇒ 2 xx 22/7 xx 7/2 xx h`

`= 154 or h = 7.`

:. Volume `= πr^2h`

`= (22/7 xx 7/2 xx 7/2 xx 7) cm^2`

`= 269.5 cm^3.`

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