Question

A soda can with a volume of 345 mL is 6.5 cm in diameter and has a mass of 20g. The can is half-filled with water, and when it is placed in a tub of water it is found to float upright. What length of the can is above the water level?

Answer 1

Answer:

0.0473m

Explanation:

345 ml = 0.000354 m3

6.5 cm = 0.065 m

20g = 0.02 kg

Since can is half filled with water, the water volume is 0.000354 / 2 = 0.000177 m cubed

Let water density be 1000kg/m3, the mass of this half-filled water is

1000*0.000177 = 0.177 kg

The total water-can system mass is 0.177 + 0.02 = 0.197 kg

For the system to stay balanced, this mass would be equal to the mass of the water displaced by the can submerged

The volume of water displaced, or submerged can is

0.197 / 1000 = 0.000197 m cubed

Then the volume of the can that is not submerged, aka above water level is

0.000354 - 0.000197 = 0.000157 m cubed

The base area of the can is

$A = \pi r^2 = \pi (d/2)^2 = \pi (0.065)^2 = 0.003318 m squared$

The length of the can that is above water is

0.000157 / 0.003318 = 0.0473 m