Question

A hollow cylindrical container has an inner radius of 7.3040 cm as stated from the manufacturer. The height of container is measured to be 20.50 cm. The thickness of the container walls can be neglected. For each part, round the final answer to the correct number of significant figures. a) Calculate the volume of this cylinder with the correct number of significant figures and units of . b) The container is filled to the top with water. The water molecules are approximated to be spheres with a diameter of 2.75 angstroms. Estimate to within one order of magnitude how many water molecules are present inside of the container. c) If the density of water is 1,000.0 kg/ , determine the mass of the water inside of the container. d) Two numbers, each having two significant figures, are added together. Is it possible for the sum to have three significant figures? Show an example and explain.

Answer 1

a) Let r be the radius such that r = 7.3040 cm and h be the height of the cylinder such that h = 20.50 cm
The volume of the cylinder will be given by V = r² h

V = (7.3040)² (20.50) = 3435.77933162 cm³
Now the least significant figures in the product we used are 3 significant figures in 20.50 cm
So the result must have not more than 3 significant figures.
So, V = 3.43 * 10³ cm³

b) Let the number of water molecules be n
Then Total Volume of water molecules = n * 4/3 r³ = Total Volume of Cylinder V
Here r = 2.75 / 2 Angstroms = 1.375 Angstroms

n * 4/3 r³ = 3.43 * 10³
n = 3.43 * 10³ / (4/3 r³ ) = 3.43 * 10³ / [4/3 (1.375*10^-10)³] = 3.1499047 * 10³²

Estimating we get n = 31 * 10³¹ number of molecules

c) Density d = 1000.0 Kg/m³
Less Mass be M kg
Now V = 3.43 * 10³ / 10⁶  m³ [ divide the volume value in cm³ by 10⁶ to get it in m³ ]
So, V = 3.43 * 10^-3  m³
As , d = M/V
or, 1000.0 = M/ 3.43 * 10^-3
or, M = 1000.0 * 3.43* 10^-3
So, M = 3.43 Kg

d) Yes it is possible to have the result of 3 significant figures when two numbers of 2 significant numbers are added.
For example, Take two numbers 99 and 12, both of these have 2 significant figures,
When we add them we get 111 which has 3 significant figures.