Question

A cylindrical metallic pipe is 14cm long.The difference between the outside and inside surfaces is 44cm square.If the pipe is made up of 99 cubic cm of metal.Find the outer and inner radii of the pipe.

Answer 1

Solution:-
Let the outer radius be 'R' and the inner radius be 'r'
Given : Height = `14 cm
Outer Surface Area  - Inner Surface Area = 44 sq cm
⇒ 2πRh - 2πrh = 44
⇒ 2*22/7(R - r) × 14 = 44
⇒ (R - r) = (44 × 7)/(44 × 14)
(R - r) = 1/2 cm  ..........(1)
Now, 
Volume of the metallic pipe = 99 cu cm
πr²h = 99 cu cm
22/7 × (R² - r²) × 14 = 99
22/7 × (R + r) × (R - r) × 14 = 99
Putting the value of (R - r) = 1/2 in the above, we get.
22/7 × (R + r) × 1/2 × 14 = 99
(R + r) = (99 × 2 × 7)/(22 × 14)
(R + r) = 99/22 = 9/2 cm ..............(2)
Adding (1) and (2), we get.
R - r + R + r = 1/2 + 9/2
R + R = 10/2
2R = 5
R = 5/2 
R = 2.5 cm
Now, 
From (2), we get.
2.5 + r = 9/2 
r = 9/2 - 2.5
r = 4/2
r = 2 cm
Hence, the outer radius is 2.5 cm and inner radius is 2 cm
Answer.

Answer 2

here ur solution....