The difference between outside and inside surface areas of cylindrical metallic pipe 14 cm long is 44 m². If the pipe is made of 99 cm³ of metal, find the outer and inner radii of the pipe.
Answers
Answer:
The outer and inner radii of the pipe are 5/2 cm and 2 cm.
Step-by-step explanation:
SOLUTION :
Let ‘r’ inner radius of the pipe & 'R' be radius of outer cylinder
Given :
Length of the cylinder (h) = 14 cm
Difference between the outer and the inner surface area of cylindrical metallic pipe= 44 cm²
Surface area of cylindrical metallic pipe = 2πh(R –r)
44 = 2πh(R –r)
44/2 = 22/7 × 14 (R –r)
22 × 7/22 = 14 (R –r)
7/14 = (R–r)
½ = (R –r)
R – r = ½ ……………..(1)
Volume of the metal used = 99 cm³,
πh(R² - r²) = 99
πh(R - r )(R + r) = 99
22/7 × 14 × (1/2)(R + r)= 99
[From eq 1]
22 (R + r)= 99
(R + r) = 99/22
(R + r) = 9/2 ……………………(2)
On adding eq 1 & 2 ,
R – r = ½
R + r = 9/2
-------------------
2R = ½ + 9/2
2R = 10/2
2R = 5
R = 5/2
On putting the value of R in eq 1,
R – r = ½
5/2 - r = ½
5/2 - ½ = r
4/2 = r
r = 2 cm
Hence, the outer and inner radii of the pipe are 5/2 cm and 2 cm.
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