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

445 cups can be filled

Explanation:

because i'm LITERALLY TAKING THE TEST AND GOT IT RIGHT...

Answer 2

Therefore,

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

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)* Height`

And For a Cone,

`\textrm{Volume of a Cone}=(1)/(3)\pi (Radius)^(2)* Height`

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

`\textrm{Number of Paper Cups}=\frac{\textrm{Volume of a Cylinder}}{\textrm{Volume of a Cone}}`

Substituting the values we get

`\textrm{Number of Paper Cups}=(\pi (r_(1))^(2)* h_(1))/((1)/(3)\pi (r_(2))^(2)* h_(2))`

Substituting the values we get

`\textrm{Number of Paper Cups}=(81* 22* 3)/(4* 3)=445.5\approx 446`

Therefore,

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