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The Height and Radius of Base of a Cylinder Area in the Ratio 3: 1. If It Volume is `1029 Pi Cm^3`; Find It Total Surface Area. - Mathematics

Sum

The height and radius of base of a cylinder area in the ratio 3: 1. if it volume is `1029 pi cm^3`; find it total surface area.

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Solution

Ratio between height and radius of a cylinder=3:1 

`"Volume" = 1029pi cm^3......(1)`

Let radium of the base=r 

then height = 3r 

`∴ "Volume"=pir^2h=pixxr^2xx3r=3pir63....(2)`

From (1) and (2) 

`3pir63=1029 pi`

`r^3=1029/3pi=343`

`r=7`

Therefore , radius = 7 cm and height =3xx7=21 cm

`"Now, total surface area "= 2pir(h+r)`

`=2xx22/7xx7xx(21+7)`

`=2xx22/7xx7xx28`

`= 1232 cm^2`

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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 20 Cylinder, Cone and Sphere
Exercise 20 (A) | Q 11 | Page 297
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