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      Question

      The difference between the external and internal curved

      surface areas of a 7 cm long cylindrical metallic pipe is 110 cm². If the pipe is made of 302.5 cm³ metal, then find the inner radius of the pipe. (Use π = 22/7)
      A 2.2 cm Correct Answer Incorrect Answer
      B 1.8 cm Correct Answer Incorrect Answer
      C 1.5 cm Correct Answer Incorrect Answer
      D 1.6 cm Correct Answer Incorrect Answer

      Solution

      Let the outer and inner radius of the pipe be R and r centimeter respectively. According to the question, 2πR × 7 - 2πr × 7 = 110   2x22/7x 7 x (R- r) =110   44(R-r) = 110 (R-r) =110/44 (R-r) = 2.5      .... (1) According to the question, π (R2 – r2) x 7 = 302.5 = 22/7 × 7 × (R2-r2) = 302.5 (R2-r2)) =302.5/22 (R2-r²) =13.75 (R+r) (R-r) = 13.75 (R+r) x 2.5 = 13.75               (From 1) (R+r) = 13.75/2.5   (R+ r) = 5.5 .... (2) Solving (1) and (2), R = 4 and r = 1.5 The inner radius of the pipe is 1.5 cm.

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