Question

The difference between inside and outside surfaces of a cylindrical tube 14 cm long is 88 sq. cm. If the volume of the tube is 176 cubic cm, find the inner and outer radii of the tube.

Answer 1

inner radius of the tube is 1.5 cm and outer radius is 2.5 cm

let radius of inner cylindrical tube is r and outer is R.

a/c to question,

2πRh - 2πrh = 88 cm²

⇒2πh(R - r) = 88 cm²

⇒2 × 22/7 × 14 (R - r) = 88 cm²

⇒R - r = 1 .........(1)

given, volume of the tube = 176 cm³

⇒πR² - πr²h = 176 cm³

⇒22/7 × 14(R² - r²) = 176 cm³

⇒(R² - r²) = 4

from equations (1) we get,

(r + 1)² - r² = 4

⇒2r + 1 = 4

⇒r = 1.5

and R = 2.5

Answer 2

We have,

2πRh−2πrh=88

⇒2π(R−r)h=88

⇒2×22/7×(R−r)×1.4=88

⇒R−r=1

And,

πR²h−πr²h=176

⇒22/7(R²−r²)×14=176⇒R²−r²=4

⇒(R+r)(R−r)=4⇒R+r=4 [∵R−r=1]

Hence, R=2.5cm and r=1.5cm.

R+r=4 cm