The difference between the outer and inner surfaces of a right circular metallic pipe. 14 cm long is 176 cm^2. if the pipe is made of 396 cm^2 metal the sum of outer and inner radii(in cm)
Answers
Answer:
Let, R be the external radius and r be the inner radius of the metallic pipe. h=14cm
Outer surface area−inner surface area=44cm2
∴2πRh−2πrh=44cm2
∴R−r=2×722×1444=2×22×1444×7
∴R−r=21.
The volume of metal used =99cm3
∴ External volume − internal volume =99cm3
∴πR2h−πr2h=99cm3
∴πh(R2−r2)=99cm3
∴722×14(R+r)(R−r)=99cm3 [∵a2−b2=(a+b)(a−b)] and [∵R−r=1/2]
22×2(R+r)21=99cm3
∴R+r=2299=29
R+r=29
2R=52R=210R−r=21
R=25=2.5cm
∴ External radius =2.5cm
R+r=29
r+2.5=4.5
r=4.5−2.5=2cm
Hence Internal radius =2cm
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Answer:
Ans : 4.5
Step-by-step explanation:
Surface area of right circular metallic pipe = 2 * π * r * h
Therefore,
2πRh-2πrh = 176
R-r = ( 176* π ) / (2 * 14)
R - r = 2
Volume of pipe = π*square(r)*h
πR2h-πr2h = 396
R2-r2 = 9
(R+r)(R-r) = 9
R+r = 9/2
Solving above two equations :
R = 13 / 4
r = 5 / 4
R + r = 4.5