A cylindrical pipe is 14cm long the difference between outer &inner surface area is44cm.sq. If the pipe is made up of 99cm.cube. of metal find outer &inner radius of pipe?
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Answers
Answer:
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.
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Answer:
2 cm and 2.5 cm
Given,
Outer surface area is 44 cm^2. Pipe is made up of 99 cm^3. height = 14 cm.
To Find,
Outer &inner radius of pipe.
Solution,
Inner radius = R and Outer radius = r, h = 14 cm.
Difference = 44 cm^2.
2πrh - 2πRh = 44
==> 2 * 22/7 * r * 14 - 2 * 22/7 * R * 14 = 44
==> R - r = 44 * 7/22 * 1/2 * 1/14
==> R - r = 1/2
Volume of pipe = 99 cm^3.
==> πR²h - πr²h = 99
==> R² - r² = 99 * 7/22 * 1/14
==> (R + r)(R - r) = 9/4
==> (R + r)(1/2) = 9/4
==> (R + r) = 9/2 ---- (2)
Add (1) and (2) .
R - r + R + r = 1/2 + 9/2
==> 2R = 5
==> R = 5/2
Place R = 5/2 in (2).
==> (R + r) = 9/2
==> 5/2 + r = 9/2
==> r = 2 cm
Result,
Outer radius = 2.5 cm and Inner radius = 2 cm.
#Hope my answer helped you.