# Cups A and B are cone shaped and have heights of #22 cm# and #23 cm# and openings with radii of #6 cm# and #12 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

So as the question posed stands cup A will overflow.

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To determine whether cup A will overflow when the contents of cup B are poured into it, we need to compare the volumes of the two cups. The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height.

First, we calculate the volume of cup A: V_A = (1/3)π(6^2)(22)

Next, we calculate the volume of cup B: V_B = (1/3)π(12^2)(23)

Now, we compare the volumes: V_A < V_B

Since the volume of cup B is greater than the volume of cup A, pouring the contents of cup B into cup A will not cause cup A to overflow. To find out how high cup A will be filled, we subtract the volume of cup A from the volume of cup B, and then divide by the base area of cup A:

Volume of liquid poured into cup A = V_B - V_A

Height filled in cup A = (Volume of liquid poured into cup A) / (π(6^2))

Substituting the values and calculating, we can find the height to which cup A will be filled.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- What is the volume of a cone with a radius of 3 and a height of 19?
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- A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #3 #, its base has sides of length #2 #, and its base has a corner with an angle of #(3 pi)/8 #. What is the pyramid's surface area?
- The base of a triangular pyramid is a triangle with corners at #(7 ,3 )#, #(4 ,1 )#, and #(3 ,2 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

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