Question

The difference between the outside and inside surfaces of a cylindrical metal pipe 14 cm long is 44 cm². If the pipe is made of 99 cm³ of metal, find the sum of the inner and outer radii of the pipe?

(a) 4.5 cm

(b) 3.5 cm

(c) 2 cm

(d) 5.5 cm

Answer 1

Correct option is (a) 4.5 cm

Let, R be the external radius and r be the inner radius of the metallic pipe. h = 14 cm

Outer surface area−inner surface area = 44 cm²

∴ 2πRh − 2πrh = 44 cm²

The volume of metal used = 99 cm³

∴ External volume − internal volume = 99 cm³

∴ πR²h − πr²h = 99 cm³

∴ πh(R² − r²) = 99 cm³

∴ \(\frac{22}7\) × 14 (R + r)(R − r) = 99 cm³ [∵ a² − b² = (a + b)(a − b)] and [∵ R − r = 1/2​]

∴ External radius = 2.5 cm

R + r = 29​

r + 2.5 = 4.5

r = 4.5 − 2.5 = 2 cm

∴ Internal radius = 2 cm

Hence, 

The sum of the inner and outer radii of the pipe = 2.5 + 2 = 4.5 cm