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.
✓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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