Question

18. The difference between outside and inside radii of a metallic cylindrical pipe of length 14 cm is 2 CM if the pipe is made of metal, find the outer and inner radii of the pipe

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Answer 1

r= inner radius 

R= outer radius 

h= height of the metallic pipe = 14 cm

Difference between the Curved surface area of the outer cylinder and Curved surface area of the inner cylinder  = 2πRh - 2πrh.

Given: 

difference between the outside and inside curved surface area of cylinder=44 cm2 .

so, 

2πh( R - r) = 44

2 x 22/ 7 x 14 ( R - r) = 44

R - r = 1 / 2 

= 0.5

Given:

the pipe is made up of metal= 99 cm³

Volume of cylindrical metallic pipe = πR²h - πr²h.

so, 

22/7 x 14 (R² - r²) = 99 

44(R² - r²) = 99

(R² - r²) = 9 / 4 

R²-r²= 2.25

( R - r)(R + r)  = 2.25

(0.5)(R + r) = 2.25

R + r = 2.25 / 0.5 

R + r  = 4.5

Adding up both the values we get

2R = 4.5 + 0.5 = 5

R = 2.5 cm and r  = 2 cm