Question

A 15cm long test tube having diameter of 3.6cm has water up to a height of 6cm .20 spherical drops of oil of radius 9mm are dropped into it.what length of the test tube remains empty?​

Answer 1

Answer:

The length of test tube that remains empty is 3 cm.

Step-by-step explanation:

Length of test tube = 15 cm

diameter of test tube = 3.6 cm

Let r be the radius of test tube. Then:

r = 1.8 cm

Let h be the height of the water in the test tube. Then:

h = 6 cm

Therefore, the volume of water inside test tube is equal to the volume of cylindrical test tube of height 6 cm equal to πr2h.

= π × 1.8 × 1.8 × 6

= π × 1810 × 1810 × 6

= π × 95 × 95 × 6 = 54150π $cm^{3}$

Radius of one spherical drop of oil (R) = 9 mm = 910 cm

Therefore volume of one spherical drop is:

= 43 πR^3 = 43π × 910 ×910 ×910 = 32403553000π $cm^{3}$

Therefore, volume of 20 spherical drops = 20 × 243π250 =

= 648071060000π $cm^{3}$

Total volume of water and oil drops = 54150π + 648071060000π

= 648071114150π $cm^{3}$

Let H be the height of mixture of water and oil in the test tube, then:

π$r^{2}$H =972π25π × 1.8 × 1.8 × H =972π25⇒1810 × 1810 × H =97225⇒8125 × H =97225⇒H =97225 × 2581 =97281 = 12 cm

Hence, the length of test tube that remains empty = 15 − 12 =3 cm.