# Cups A and B are cone shaped and have heights of #25 cm# and #18 cm# and openings with radii of #8 cm# and #3 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?

no overflow , h ≈ 2.53cm

The volume of liquid in A = 169.646

To find height of liquid solve:

multiply by 3 to eliminate fraction.

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

To determine whether cup A will overflow when the contents of cup B are poured into it, we need to compare the volumes of the two cups. Since both cups are cone-shaped, we can use the formula for the volume of a cone, which is given by:

[ V = \frac{1}{3} \pi r^2 h ]

where ( V ) is the volume, ( r ) is the radius of the base, and ( h ) is the height of the cone.

For cup A:

- Height ( h = 25 ) cm
- Radius ( r = 8 ) cm

For cup B:

- Height ( h = 18 ) cm
- Radius ( r = 3 ) cm

Now, we can calculate the volumes of both cups:

For cup A: [ V_A = \frac{1}{3} \pi (8^2) (25) = \frac{1}{3} \pi (64) (25) = \frac{1600}{3} \pi ]

For cup B: [ V_B = \frac{1}{3} \pi (3^2) (18) = \frac{1}{3} \pi (9) (18) = 54 \pi ]

Since ( V_B < V_A ), cup B's contents can fit inside cup A without overflowing. To find out how high cup A will be filled, we need to calculate the height at which the volume of cup A equals the volume of cup B:

[ \frac{1}{3} \pi (8^2) (h) = 54 \pi ] [ \frac{64}{3} \pi h = 54 \pi ] [ h = \frac{54 \pi \cdot 3}{64 \pi} ] [ h \approx \frac{162}{64} \approx 2.53 \text{ cm} ]

So, cup A will be filled to a height of approximately ( 2.53 ) cm when the contents of cup B are poured into it.

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.

- The base of a triangular pyramid is a triangle with corners at #(5 ,1 )#, #(2 ,3 )#, and #(3 ,4 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?
- 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?
- What is the circumference of the circle whose equation is #(x-9)^2+(y-3)^2=64#?
- The length of a rectangle is 3 times as great as its width. If the perimeter of the rectangle is no more than 72 cm, what is the greatest possible length of the rectangle?
- What are regular polyhedrons? Give a few examples. Can we have general formula for finding their surface areas?

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