# Cups A and B are cone shaped and have heights of #35 cm# and #29 cm# and openings with radii of #12 cm# and #16 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?

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To determine if cup A will overflow when the contents of cup B are poured into it, we need to compare the volumes of the two cones.

The volume of a cone is given by the formula ( V = \frac{1}{3} \pi r^2 h ), where ( r ) is the radius of the base and ( h ) is the height.

For cup A: Radius, ( r = 12 ) cm Height, ( h = 35 ) cm

For cup B: Radius, ( r = 16 ) cm Height, ( h = 29 ) cm

Let's calculate the volumes of the two cones:

For cup A: [ V_A = \frac{1}{3} \pi (12^2) (35) ]

For cup B: [ V_B = \frac{1}{3} \pi (16^2) (29) ]

After finding the volumes, we can compare them to see if cup A can hold the contents of cup B without overflowing. If cup A's volume is greater than or equal to cup B's volume, then cup A will not overflow. Otherwise, it will overflow.

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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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