Question

The difference between outside and inside surface of a cylindrical metallic

pipe 14m long is 44 cm2. If the sum of the diameters of the inner and outer

surface of the cylinder is 9 cm, find the inner and outer radii of the cylinder​

Answer 1

The difference between outside and inside surfaces of a cylindrical metallic pipe 14cm long is 44 cm

2

. If the pipe is made of 99 cm

3

of metal, find the outer and inner radii of the pipe.

Medium

Solution

verified

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Let, R be the external radius and r be the inner radius of the metallic pipe. h=14cm

Outer surface area−inner surface area=44cm

2

∴2πRh−2πrh=44cm

2

∴R−r=

2×

7

22

×14

44

=

2×22×14

44×7

∴R−r=

2

1

.

The volume of metal used =99cm

3

∴ External volume − internal volume =99cm

3

∴πR

2

h−πr

2

h=99cm

3

∴πh(R

2

−r

2

)=99cm

3

∴

7

22

×14(R+r)(R−r)=99cm

3

[∵a

2

−b

2

=(a+b)(a−b)] and [∵R−r=1

/2

]

22×2(R+r)

2

1

=99cm

3

∴R+r=

22

99

=

2

9

R+r=

2

9

2R=5

2R=

2

10

R−r=

2

1

R=

2

5

=2.5cm

∴ External radius =2.5cm

R+r=

2

9

r+2.5=4.5

r=4.5−2.5=2cm

Hence Internal radius =2cm