the difference between the outside and inside surfaces of a cylindrical metallic pipe 14 cm^2 long is 44 cm^2 if the sum of the inner and outer radii be 3\2 find the outer and inner radii of the pipe
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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
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