a 15 cm long test tube having diameter of 3.6cm has water up to a height of 6cm . 20 spherical drops of oils of radius 9mm are dropped into it. What length of test tube remains empty?
Answers
Answer:
3 cm
Explanation:
the volume of water inside test tube is equal to the volume of cylindrical test tube of height 6 cm equal to πr2h. Hence, the length of test tube that remains empty = 15 − 12 =3 cm
Please mark me as brainliest
Height of the test tube = 15cm
Diameter of the test tube= 3.6 cm
Radius of the test tube = 3.6/2 cm = 1.8 cm
Volume of the test tube= πr²h
= (3.14×1.8×1.8×15) cm³
= 152.604 cm²
Height of the water in the test tube = 6cm
Volume of water in the test tube= πr²h
= (3.14 × 1.8×1.8×6) cm³
= 61.04 cm³
Volume of test tube remain empty = (152.604 -61. 04) cm³
= 91.564 cm³
Radius of the oil drop = 9mm= 9/10 cm = 0.9cm
Volume of oil drop = 4/3 πr³
= (4/3×3.14×0.9×0.9×0.9) cm³
= 3.05 cm³
Volume of 20 oil drop = (20×3.05) cm³ = 61 cm³
Volume of test tube remain empty after pouring oil in the test tube = (91.564 - 61) cm³
= 30.564 cm³
Let the height of the empty test tube be h
therefore, we know that,
volume of cylinder = πr²h
30.564= 3.14 × 1.8×1.8 ×h
or 3= h
Length of the test tube remains empty = 3 cm