Answer :
Given :
Diameter of the flask = 25 cm
radius, r = [tex]$\frac{25}{2}$[/tex] cm
Height of the flask, h = 40 cm
We have to find out the volume of the cylinder flask
Volume [tex]$= \pi r^2h$[/tex]
[tex]$= 3.14 \times (\frac{25}{2})^2 \times 40$[/tex]
= [tex]$19634.95 \ cm^3$[/tex]
= [tex]$19635 \ cm^3$[/tex]
Now calculate the volume of the marble
Given :
Diameter = 13 mm
radius, R [tex]$=\frac{13}{2} \ mm$[/tex]
Therefore, volume of the marble [tex]$=\frac{4}{3}\pi R^3$[/tex]
[tex]$=\frac{4}{3}\times 3.14 \times (\frac{13}{2})^3$[/tex]
[tex]$= 1150.35 \ mm^3$[/tex]
or [tex]$= 115.035 \ cm^3$[/tex]
Therefore, the number of the marbles [tex]$=\frac{\text{volume of flask}}{\text{volume of marble}}$[/tex]
[tex]$=\frac{19635}{115.035}$[/tex]
= 170.68
Therefore, the number of the marbles used is approximately 170.