Question

The difference between outside and inside surface of a cylindrical metallic tripe 14cm. long is 44 sq.cm. If the tripe is made of 99 cu. cm. of metal, find the outer and inner radius of the pipe.

Answer 1

Let r1 and r2 be the inner and outer radius of the cylindrical metallic pipe.

Height of the metallic pipe = 14 cm

Difference between the curved surface area of the outer cylinder and the inner cylinder = 2π(r2)h - 2π(r1)h & Given that, 2π(r2)h - 2π(r1)h = 44 cm².

So, 2πh(r2 - r1) = 44
44/7 x 14 (r2 - r1) = 44
r2 - r1 = 1 / 2 = 0.5 (i)

Given that, pipe is made up of 99 cm³ of metal.

So, volume of cylindrical metallic pipe = π(r2)2h - π(r1)2h.
=22/7 x 14 {(r2)² - (r1)²} = 99 cm³
= 44 x {(r2²) - (r1²)} = 99
= (r2 - r1) = 99 / 44 = 2.25
= (r2 - r1)(r2 + r1) = 2.25
= (0.5) x (r2+ r1) = 2.25
r2 + r1 = 2.25 / 0.5 = 4.5
r2 + r1 = 4.5 (ii)

Adding (i) & (ii) we get,
2(r2) = 4.5 + 0.5
r2 = 5/2
r2 = 2.5 cm Ans.

Therefore, r1 + r2 = 4.5
r1 + 2.5 = 4.5
r1 = 4.5 - 2.5
r1 = 2 cm Ans.

Ans.) The Outer radius r2 is 2.5 cm and inner radius r1 is 2 cm.

Answer 2

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