# Cups A and B are cone shaped and have heights of #27 cm# and #23 cm# and openings with radii of #7 cm# and #10 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?

cup A will overflow.

The first step is to calculate the volumes ( V) of both cups.

By signing up, you agree to our Terms of Service and Privacy Policy

No, cup A will not overflow. When the contents of cup B are poured into cup A, the volume of cup A will increase but will not exceed its capacity. To find out how high cup A will be filled, we need to calculate the increase in volume when the contents of cup B are poured into it. Then, we can use the formula for the volume of a cone to find the corresponding height.

The volume of a cone is given by the formula: [ V = \frac{1}{3} \pi r^2 h ]

We can calculate the volumes of cups A and B using their respective heights and radii. Then, we find the difference in volume when cup B is poured into cup A. Using this difference in volume, we can calculate the corresponding increase in height of cup A.

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.

- Two corners of a triangle have angles of #(3 pi ) / 8 # and # pi / 8 #. If one side of the triangle has a length of #5 #, what is the longest possible perimeter of the triangle?
- 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 #6 #, its base's sides have lengths of #5 #, and its base has a corner with an angle of #(5 pi)/8 #. What is the pyramid's surface area?
- A triangle has two corners with angles of # ( pi ) / 3 # and # ( pi )/ 6 #. If one side of the triangle has a length of #8 #, what is the largest possible area of the triangle?
- Two corners of an isosceles triangle are at #(3 ,9 )# and #(2 ,7 )#. If the triangle's area is #4 #, what are the lengths of the triangle's sides?
- How do you derive the formula for the area of an equilateral triangle?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7