A cylindrical metallic pipe is 14 cm long. The difference between the outside and inside surfaces is 44 cm. If the pipe is made up of 99 cu cm of metal, find the outer and inner radii of the pipe.
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A cylindrical metallic pipe is 14 cm long. The difference between the outside and inside surfaces is 44 cm. If the pipe is made
Step-by-step explanation:
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