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Solve this question!!
"A cylindrical Metallic pipe is 14cm long.The difference between the outside and inside surfaces is 44cm^2 .If the pipe is made up of 99 cu cm of metal , find the outer and inner radii of the pipe."
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Answers
Given that cylindrical metallic pipe h = 14 cm.
(i)
Given that difference between the outside and inside surfaces is 44 cm^2.
⇒ 2πRh - 2πrh = 44
⇒ 2πh(R - r) = 44
⇒ 2 * (22/7) * 14(R - r) = 44
⇒ 88(R - r) = 44
⇒ (R - r) = 44/88
⇒ (R - r) = 1/2 ------ (1)
(ii)
Given that volume of outer part - volume of inner part = 99 cm^3.
⇒ πh(R^2 - r^2) = 99
⇒ (22/7) * 14(R^2 - r^2) = 99
⇒ 44(R^2 - r^2) = 99
⇒ R^2 - r^2 = 99/44
⇒ R^2 - r^2 = 9/4
We know that a^2 - b^2 = (a + b)(a - b)
⇒ (R + r)(R - r) = 9/4
⇒ (R + r) * (1/2) = 9/4
⇒ (R + r) = 9/2 -------- (2)
On solving (1) & (2), we get
⇒ R - r = 1/2
⇒ R + r = 9/2
---------------
2R = 10/2
2R = 5
R = 2.5 cm.
Substitute R = 2.5 in (1), we get
⇒ R - r = 1/2
⇒ 2.5 - r = 1/2
⇒ -r = 1/2 - 2.5
⇒ -r = -2
⇒ r = 2.
Therefore:
⇒ Outer radii of the pipe = 2.5 cm.
⇒ Inner radii of the pipe = 2 cm.
Hope it helps! ----- > Good luck!
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