Question

A cylindrical metallic pipe is 14cm long. The difference between the outside and inside surface areas is 44cm². If the pipe is made up of 99cm³ of metal, find the putter and inner radio 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