Question

an office cooler has the shape of a cylinder with a radius of 9 in the height of the cooler is 22in water is dispensed into paper cups that have the shape of a cone with a radius of 2 in the height of each paper cup is 3 in what is the greatest number of paper cups that can be completely filled from the water cooler

Answer 1

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

$\textrm{Volume of a Cylinder}=\pi (Radius)^{2}\times Height$

And For a Cone,

$\textrm{Volume of a Cone}=\dfrac{1}{3}\pi (Radius)^{2}\times Height$

Now number of paper cups that can be completely filled from the water cooler will be given as

$\textrm{Number of Paper Cups}=\dfrac{\textrm{Volume of a Cylinder}}{\textrm{Volume of a Cone}}$

Substituting the values we get

$\textrm{Number of Paper Cups}=\dfrac{\pi (r_{1})^{2}\times h_{1}}{\dfrac{1}{3}\pi (r_{2})^{2}\times h_{2}}$

Substituting the values we get

$\textrm{Number of Paper Cups}=\dfrac{81\times 22\times 3}{4\times 3}=445.5\approx 446$

Therefore,

The greatest number of paper cups that can be completely filled from the water cooler is 446 cups.