# 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.

#### 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