Question

The difference between outside and inside surface areas of cylindrical metallic pipe 14
cm long is 44 m². If the pipe is made of 99 cm³ of metal, find the outer and inner radii of
the pipe.
​

Answer 1

Answer:

given: L = 14 cm, CSA1 - CSA2 = 44cm², Volume of metal V = 99cm³

to find R and r

Step-by-step explanation:

formula used: CSA1 - CSA2 = 2πh( R - r)

=> 2×22/7×14(R - r) = 44

=> R - r = (44×7) / 2×22×14

=> R - r = 1/2........1

V = πh(R² - r²)

99 = 22/7 × 14 ( R² - r²)

=> R² - r² = (99×7) / 22 × 14

=> R² - r² = 9×7/2×14 => 9/4......... 2

R² - r² = (R + r)(R - r)

9/4 = (R+r)(1/2) [ from 1 ]

=> R + r = 9/4 × 2/1

=> R + r = 9/2.......3

solving equations 1 and 3,

=> R - r = 1/2

=> R + r = 9/2

=> 2R = 5

=> R = 2.5 cm

=> 5/2 - r = 1/2

=> r = 5/2 - 1/2 = 2 cm

R = 2.5 cm and r = 2 cm