Cups A and B are cone shaped and have heights of #35 cm# and #23 cm# and openings with radii of #14 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?

Answer 1

cup #A# will not overflow.

#=28.5# cm

Total volume of cup #B=pir^2h/3=pi(9)^2(23/3)=621pi# Total volume of cup #A=pir^2h/3=pi(14)^2(35/3)=2286.67pi# Since volume of cup #B# is less than volume of cup #A#; Contents of cup #B# if poured into cup #A# will not make cup #A# overflow hence cup #A# will not overflow.
So we have to find #H=?# the height in Cup #A# which will have content of same volume as volume of Cup#B#
#pi(14)^2(H/3)=pi(9)^2(23)# or
#H/3=(9^2/14^2)(23)=9.5# or
#H=28.5# cm
Sign up to view the whole answer

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

Sign up with email
Answer 2

Yes, cup A will overflow when the contents of cup B are poured into it. To find out how high cup A will be filled, you can calculate the volume of cup B's contents and compare it to the volume of cup A.

The volume of a cone can be calculated using the formula: ( V = \frac{1}{3} \pi r^2 h ), where ( r ) is the radius and ( h ) is the height.

First, calculate the volume of the contents of cup B using its dimensions. Then, compare this volume to the volume of cup A. If the volume of cup B's contents is greater than the remaining volume in cup A after pouring, cup A will overflow. Otherwise, cup A will be filled to the height of its remaining volume after pouring.

Sign up to view the whole answer

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

Sign up with email
Answer from HIX Tutor

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7