Question

Question - 82
The difference between outside and inside surface of a cylindrical mettalic pipe 14cm long is 44 sq cm.
If the pipe is made of 99 cu cm of metal, find the outer and inner radii of the pipe.

Answer 1

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

Answer 2

Heya,

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

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.

HOPE IT HELPS:-))