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Answers
Question
The difference between the outer and inner curved surface areas of a hollow right circular cylinder 14cm long is 88cm². If the volume of metal used in making cylinder is 176cm³. Find outer and inner diameters of the cylinder?
Answer
Inner and outer radii of hollow right circular cylinder is 1.5 and 2.5 cm.
Explanation
Let the inner and outer diameter of hollow cylinder be 'd' and 'D'.
So, inner radii will be 'r' and outer radii will be 'R'.
Curved surface of hollow cylinder = 2π(R - r)h
We have given that, height of hollow cylinder is 14 cm and difference between inner and outer surface is 88 cm².
Substitute the known values in above formula
⇒ 88 = 2π(R - r)14
⇒ 44 = 22/7 × (R - r)14
⇒ 44 = 22 × 2(R - r)
⇒ 44 = 44(R - r)
⇒ 1 = R - r
⇒ R - r = 1 ....(eq 1)
Also,
Volume of hollow cylinder = π(R² - r²)h
We have given that, volume of metal used in making cylinder is 176cm³.
Substitute the known values in above formula
⇒ π(R² - r²) × 14 = 176
⇒ 22/7 × 14(R² - r²) = 176
⇒ 44(R² - r²) = 176
⇒ R² - r² = 4
Used identity: (a + b)(a - b) = a² - b²
⇒ (R + r)(R - r) = 4
⇒ (R + r)(1) = 4
⇒ R + r = 4 ....(eq 2)
Add (eq 1) and (eq 2)
⇒ R + r + R - r = 4 + 1
⇒ 2R = 5
⇒ R = 5/2
Outer radii of hollow cylinder is 5/2 or 2.5 cm.
Substitute value of R = 5/2 in (eq 1)
⇒ 5/2 - r = 1
⇒ - r = 1 - 5/2
⇒ - r = (2 - 5)/2
⇒ - r = -3/2
⇒ r = 3/2
Inner radii of hollow cylinder is 3/2 or 1.5 cm.
Answer:
R=5/2
r=3/2
Step-by-step explanation:
please see the pic for the answer.
