Cups A and B are cone shaped and have heights of 27 cm and 21 cm and openings with radii of 7 cm and 11 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?
1 Answer
Aug 20, 2016
cup A will overflow.
Explanation:
We require to compare the
color(blue)"volumes" of the 2 cups.The
color(blue)"volume(V) of a cone " is
color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(V=1/3pir^2h)color(white)(a/a)|)))
where r, is the radius and h, is the height.
rArrV_(A)=(pixx7^2xx27)/3≈1385.442" cubic cm" and
V_(B)=(pixx11^2xx21)/3≈2660.293" cubic cm" Since volume of cup B > volume of cup A, when the contents of B are poured into A, it will overflow.