Let r and R be the inner and outer radius of the cylindrical metallic pipe respectively.
h be the 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 that difference between the outside and inside curved surface area of cylinder is 44 cm2.
⇒ 2πh(R - r) = 44
⇒ \(\frac{44}7\) × 14 (R - r) = 44
⇒ R - r = \(\frac 12\) = 0.5 ----------(1)
Given the pipe is made up of 99 cubic cm of metal so that
Volume of cylindrical metallic pipe = πR2h - πr2h.
⇒ \(\frac{22}7\) × 14 (R2 - r2) = 99 cm3 .
⇒ 44 × (R2 - r2) = 99
⇒ (R2 - r2) = \(\frac 94\) = 2.25
⇒ (R - r)(R + r) = 2.25
= (0.5) × (R + r) = 2.25
R + r = \(\frac{2.25}{0.5}\) = 4.5
R + r = 4.5 ------------ (2)
Adding (1) and (2) we get
2R = 4.5 + 0.5 = 5
∴ R = 2.5 cm and r = 2 cm
∴ Outer side radius R = 2.5 cm and inner side radius r = 2 cm.