The difference between outside and inside surfaces of a cylindrical metallic pipe of 14 cm long is 44 cm square. If the pipe is made of 44 cm cube of metal, find the outer and inner radii of the pipe.
Answers
Answer:
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
Step-by-step explanation:
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Answer:
Step-by-step explanation:
Let, R be the external radius and r be the inner radius of the metallic pipe. h=14cm
Outer surface area−inner surface area=44cm
2
∴2πRh−2πrh=44cm
2
∴R−r=
2×
7
22
×14
44
=
2×22×14
44×7
∴R−r=
2
1
.
The volume of metal used =99cm
3
∴ External volume − internal volume =99cm
3
∴πR
2
h−πr
2
h=99cm
3
∴πh(R
2
−r
2
)=99cm
3
∴
7
22
×14(R+r)(R−r)=99cm
3
[∵a
2
−b
2
=(a+b)(a−b)] and [∵R−r=1
/2
]
22×2(R+r)
2
1
=99cm
3
∴R+r=
22
99
=
2
9
R+r=
2
9
2R=5
2R=
2
10
R−r=
2
1
R=
2
5
=2.5cm
∴ External radius =2.5cm
R+r=
2
9
r+2.5=4.5
r=4.5−2.5=2cm
Hence Internal radius =2cm