QQuestion
Difference of outer and inner curved surface area of a hollow cylindrical pipe is 44 sq.cm and length is 14 cm. If the Volume of the material of the pipe be 99 cubic cm. Find inner and outer radius.
WBBSEClass 10MathematicsRight Circular Cylinder04 Mark2024 Moderate
✓Answer
Let the outer radius = R and length (h) = 14 cm
2πRh – 2πrh = 44
⇒ 2πh (R – r) = 44
⇒ 2 × 22\over 7 × 14 × (R – r) = 44
⇒ R – r = 44 × 7\over 2 × 22 × 14
⇒ R – r = 1\over 2 —- (i)
Volume of metal = 99 cm³
⇒ π(R² – r²)h = 99
⇒ π(R² – r²)h = 99
⇒ π(R – r)(R + r)h = 99
⇒ R + r = 9\over 2 —- (ii)
Solve equation (i) and (ii) to get
R = 5\over 2 cm and r = 2 cm
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