Question

the inner and outer radii of a cylindrical pipe are 4cm and 5cm respectively find the area of cross section of the pipe ​

Answer 1

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

⇒ 44 / 7 x 14 ( R - r) = 44

⇒ R - r = 1 / 2 = 0.5 ----------(1) Given the pipe is made up of 99 cubic cm of metal so that

Volume of cylindrical metallic pipe = πR2h - πr2h.

⇒ 22/7 x 14 (R2 - r2) = 99 cm3 .

⇒ 44 x (R2 - r2) = 99

⇒ (R2 - r2) = 9 / 4 = 2.25

⇒ ( R - r)(R + r) = 2.25

= (0.5)x(R + r) = 2.25

R + r = 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.