Question

The difference between outside and inside surface of a cylindrical
metallic pipe 14m long is 44 cm2. If the sum of the diameters of the
inner and outer surface of the cylinder is 9 cm, find the inner and
outer radii of the cylinder

Answer 1

Answer:

Step-by-step explanation:

r= inner radius

R= outer radius

h= 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:

difference between the outside and inside curved surface area of cylinder= 44 cm2 .

so,

2πh( R - r) = 44

2 x 22/ 7 x 14 ( R - r) = 44

R - r = 1 / 2

= 0.5

Given:

the pipe is made up of metal= 99 cm³

Volume of cylindrical metallic pipe = πR²h - πr²h.

so,

22/7 x 14 (R² - r²) = 99

44(R² - r²) = 99

(R² - r²) = 9 / 4

R²-r²= 2.25

( R - r)(R + r)  = 2.25

(0.5)(R + r) = 2.25

R + r = 2.25 / 0.5

R + r  = 4.5

Adding up both the values we get

2R = 4.5 + 0.5 = 5

R = 2.5 cm and r  = 2 cm