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
By signing up, you agree to our Terms of Service and Privacy Policy
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.
By signing up, you agree to our Terms of Service and Privacy Policy
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.
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?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7