Question

the difference between inside and outside surfaces of a 14 cm long cylindrical tube is 88 squares and if the volume of the tube is 176 cubic centimetre find the inner and outer raddi of the tube​

Answer 1

Given: Let r

1

be the radius of inner tube, r

2

be the radius of outer tube

⇒2πr

2

h−2πr

1

h=88 sq. cm

⇒2π(r

2

−r

1

)h=88

⇒2×

7

22

(r

2

−r

1

)×14=88

⇒r

2

−r

1

=1 ………….(1)

Volume of the tube = volume of outer tube − volume of inner tube

=πr

2

2

h−πr

1

2

h

=π(r

2

2

−r

1

2

)h=π(r

2

−r

1

)(r

2

+r

1

)h from (1)

4=π(r

1

+r

2

)×14

⇒176=

7

22

(r

1

+r

2

)×14

⇒r

1

+r

2

=4 ……..(2)

From (1) & (2)

r

1

+r

2

+r

2

−r

1

=4+1

⇒2r

2

=5

⇒r

2

=

2

5

=2.5cm

From (2)

r

1

=4−r

2

=(4−2.5)cm

=1.5cm

∴ Inner radius r

1

=1.5cm

Inner diameter =2r

1

=2×1.5

=3cm.