# Cups A and B are cone shaped and have heights of #24 cm# and #23 cm# and openings with radii of #11 cm# and #9 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?

Volume of a cone is given by

Volume of cone A is

Volume of cone B is

It is obvious that when contents of a full cone B are poured into cone A, it will not overflow. Let it reach where upper circular surface will form a circle of radius

then the relation becomes

So equating

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Yes, cup A will overflow. If the contents of cup B are poured into cup A, the liquid will overflow because the volume of cup B is greater than the volume of cup A. Therefore, cup A will not be able to contain all the liquid from cup B, and 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.

- A cylinder has a radius of 4 inches and a side surface area of 150.72 inches. What is the surface area of the cylinder?
- A cone has a height of #9 cm# and its base has a radius of #6 cm#. If the cone is horizontally cut into two segments #7 cm# from the base, what would the surface area of the bottom segment be?
- Cups A and B are cone shaped and have heights of #32 cm# and #21 cm# and openings with radii of #13 cm# and #11 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?
- Two corners of a triangle have angles of #pi / 3 # and # pi / 2 #. If one side of the triangle has a length of #7 #, what is the longest possible perimeter of the triangle?
- One end of a guy wire will attach to a telephone pole 10 feet above the ground. The other end of the guy wire will attach to a bracket located 30 feet from the base of the pole. How long of a guy wire is needed?

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