Question

the radius and the height of a cylinder are in ratio 7:3 ,if the volume of the cylinder is12474cm cube find the curved surface Area and the total surface area of cylinder

Answer 1

let the radius of cylinder= r cm and
the height = h cm

rato of r and h = 7:3

r / h = 7 /3 => r = 7h/ 3

volume = 12474

πr^2h = 12474

(22/ 7) × ( 7h/ 3)^2 × h = 12474

154 h^3 / 9 = 12474

h^3 =( 12474 × 9)/ 154

h^3 = 81 × 9 = 729

h = 9 cm , r = 7h/ 3 = (7 × 9)/ 3 = 21 cm

c.s.a of cylinder = 2πrh

= (2 × 22 × 21 × 9 ) ÷ 7 = 1188 cm^2

total surface area of cylinder

= 2πr ( r + h ) = 2 × (22/ 7) × 21 ( 21 + 9)

= 44 × 3 × 30 = 3960 cm^2

Answer:
-------------

c.s.a = 1188cm^2, t.s.a = 3960 cm^2

Answer 2

Step- by-Step Solution

Volume of cylinder =12474 cm³

Let the no. be =7x,3x

So,

Step

Volume=πr²h

12474=22/7*7x*7x*3x

12474=22*x*7x*3x

12474=22*21x³

21x³=12474/22

21x³=567

x³=567/21

x³=27

x=√27

x=3 cm

Therefore,

r=7x

r=7*3

r=21 cm

h=3x

h=3*3

h=9 cm

So,

Curved S.A=2πrh

=2*22/7*21*9

=44*27

=1188 cm²

T.S.A=2πrh+2πr²

=1188 cm²+2*22/7*21*21

=1188 cm²+44*63

=1188 cm²+2772 cm²

=3960 cm²

Answer-

r=21 cm h=9 cm

Curved S.A=1188 cm²

T.S.A=3960 cm²