Answer:
Therefore,
The greatest number of paper cups that can be completely filled from the water cooler is 446 cups.
Step-by-step explanation:
For Cylinder Cooler
Radius = r₁ = 9 in
Height = h₁ = 22 in
For Cone Cups,
Radius = r₂ = 2 in
Height = h₂ = 3 in
To Find:
Number of Paper Cups = ?
Solution:
For a Cylinder we know that
[tex]\textrm{Volume of a Cylinder}=\pi (Radius)^{2}\times Height[/tex]
And For a Cone,
[tex]\textrm{Volume of a Cone}=\dfrac{1}{3}\pi (Radius)^{2}\times Height[/tex]
Now number of paper cups that can be completely filled from the water cooler will be given as
[tex]\textrm{Number of Paper Cups}=\dfrac{\textrm{Volume of a Cylinder}}{\textrm{Volume of a Cone}}[/tex]
Substituting the values we get
[tex]\textrm{Number of Paper Cups}=\dfrac{\pi (r_{1})^{2}\times h_{1}}{\dfrac{1}{3}\pi (r_{2})^{2}\times h_{2}}[/tex]
Substituting the values we get
[tex]\textrm{Number of Paper Cups}=\dfrac{81\times 22\times 3}{4\times 3}=445.5\approx 446[/tex]
Therefore,
The greatest number of paper cups that can be completely filled from the water cooler is 446 cups.
