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.
WBBSE
Class X
Mathematics
Right Circular Cylinder
04 Mark
2024
Let the outer radius = R and length (h) = 14 cm
2Ï€Rh – 2Ï€rh = 44
⇒ 2Ï€h (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
⇒ Ï€(R² – r²)h = 99
⇒ Ï€(R² – r²)h = 99
⇒ Ï€(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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