Question

To measure the volume of a coin, water is taken in a measuring cylinder to a level 15.0 ml. On immersing the coin in it, the water level in the measuring cylinder rises to 16.7ml. What is the volume of coin? Express your result in S.I units.

Answer 1

Hint - We will use Archimedes’ principle which is helpful in finding out the changes caused to the volume of the liquid when a coin is immersed in a liquid. Now as we have the quantities of the change in volume, we can easily calculate the volume of the coin.

Complete step-by-step answer:
The volume of the cylinder is measured by the formula $V = \pi {r^2}h$, where $r$ is the radius and $h$ is the thickness of height. If you have a Vernier caliper you should be able to measure the dimension quite accurately. The ruler will give an approximate result.
By using the displacement method, we can measure the amount displaced.

Archimedes' principle - An object immersed in a fluid undergoes a buoyant force that is equal in magnitude to the force of gravity on the replaced fluid.

Archimedes’ principle states that the upward force that is employ on a body on a body immersed in a fluid, whether fully or partially submerged is equal to the weight of the fluid that the body displaces

$1\,millilitre = {10^{ - 6}}{m^3}$ (Conversion of Units)
Variation in volume after the coin is immersed
$= 16.7 - 15 = 1.7ml = 1.7 \times {10^{ - 6}}{m^3}$

Note - A submerged object evicts a volume of liquid equal to the volume of the object. One milliliter of water has a volume of one cubic centimeter, also measure the volume by calculating the amount of liquid the coin evicts, but this would not be so accurate due to the surface tension, and you would need a calibrated measuring glass.