Respuesta :
3042 droplets of water with a radius of 2 mm must fall into the jar to be full.
Given,
A glass jar has the shape of a straight circular cylinder.
- inner radius of 26mm.
- inner height of 48mm.
Water droplets
- radius of 2 mm
We need to find how many droplets of water are needed to fill the jar full.
We assume that the drops are spherical.
What is the volume of a cylinder and a sphere?
The volume of the cylinder = [tex]\pi[/tex] r²h
The volume of the sphere = 4/3 [tex]\pi[/tex] r³
We have,
Glass jar = straight circular cylinder
Drops of water = sphere
In order to fill the cylindrical shape jar with droplets of water the volume of water droplets must be equal to the volume of the jar.
The volume of the jar:
r = 26 mm
h = 48 mm
= [tex]\pi[/tex] r²h
= [tex]\pi[/tex] 26² 48
= [tex]\pi[/tex] x 676 x 48
= 32448[tex]\pi[/tex]
The volume of the droplets of water:
r = 2 mm
= 4/3 [tex]\pi[/tex] r³
= 4/3 x [tex]\pi[/tex] x 2³
= 4/3 x [tex]\pi[/tex] x 8
= 32/3[tex]\pi[/tex]
We see that,
D x 32/3[tex]\pi[/tex] = 32448[tex]\pi[/tex]
Where D is the number of droplets.
Finding D value.
D x 32/3[tex]\pi[/tex] = 32448[tex]\pi[/tex]
D = (32448 x 3)/ 32
D = 3042
Thus 3042 droplets of water with a radius of 2 mm must fall into the jar to be full.
Learn more about the Volume of the sphere here:
https://brainly.com/question/9994313
#SPJ1
