# Cups A and B are cone shaped and have heights of #27 cm# and #25 cm# and openings with radii of #7 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?

Yes, cup A will overflow.

Since cone B has a greater volume than cone A, and it is given that cone B is completely full, it can be concluded that cup A will overflow.

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

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 cups.

The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height.

For cup A: Volume of cup A = (1/3) * π * (7 cm)^2 * 27 cm

For cup B: Volume of cup B = (1/3) * π * (9 cm)^2 * 25 cm

Calculate the volumes of both cups using these formulas.

If the volume of cup B is less than or equal to the remaining volume in cup A after pouring, then cup A will not overflow. Otherwise, it will overflow.

Once the volumes are calculated, if cup A does not overflow, you can find how high it will be filled by subtracting the volume of cup B from the remaining volume of cup A, and then dividing by the area of the base of cup A (πr^2). This will give you the height of the liquid in 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 circles having equal radii #r_1# and touching a line #l#on the same side of #l# are at a distance of #x# from each other. Third circle of radius #r_2# touches the two circles. How do we find the height of third circle from #l#?
- A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #3 # and #2 # and the pyramid's height is #6 #. If one of the base's corners has an angle of #pi/4 #, what is the pyramid's surface area?
- I need an expression in simplest form for the perimeter of a triangle, left side of the triangle says 2x bottom line says 4x-2 and right side says 2x+3?
- The perimeter of a regular hexagon is 48 inches. What is the number of square inches in the positive difference between the areas of the circumscribed and the inscribed circles of the hexagon? Express your answer in terms of pi.
- A rectangle has asides of 4.2 and 6.7. What is its perimeter?

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