Cups A and B are cone shaped and have heights of #39 cm# and #22 cm# and openings with radii of #17 cm# and #13 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?

Question

Cups A and B are cone shaped and have heights of #39 cm# and #22 cm# and openings with radii of #17 cm# and #13 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?

Claire Akin · Accepted Answer

cup #A# will not overflow.
#Height=12.865# cm

Total volume of cup #B=pir^2h/3=pi(13)^2(22/3)=1239.33pi# Total volume of cup #A=pir^2h/3=pi(17)^2(39/3)=3757pi# 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(17)^2(H/3)=1239.33pi# or #H/3=1239.33/17^2=4.288# or #H=12.865# cm

Aaliyah Anderson · Answer

undefined No, cup A will not overflow. When cup B is poured into cup A, the volume of cup B will fit within cup A because the volume of cup B is less than the volume of cup A. The final height of cup A will be the sum of its original height and the height of the liquid poured from cup B. To find the height of the liquid in cup A after pouring from cup B, you need to calculate the volume of cup B and then use the formula for the volume of a cone to find the height of the liquid in cup A. The formula for the volume of a cone is V = (1/3) * π * r^2 * h, where V is the volume, π is pi (approximately 3.14159), r is the radius, and h is the height. Calculate the volume of cup B using its dimensions and then use the volume to find the height of the liquid in cup A.