Problema Solution
a punch bowl is in the shape of a hemisphere with the diameterof 20 inches and is filled with a tropical dring. How many cups shaped like an inverted cone with the height of 4 inches and a radius of 2 inches can be filled from this punch bowl?
Answer provided by our tutors
Volume of hemisphere: (2/3) * pi * r^3
r = 20 in / 2 = 10 in
Volume_h = 2/3 * pi * 1000 in^3 = 2000 * pi / 3 in^3
Volume of cone: (1/3) * pi * r^2 * h
Volume_c = 1/3 * pi * 4 in^2 * 4 in = 16 * pi / 3 in^3
Volume_c / Volume_h = 2000 / 16 = 1000 / 8 = 500 / 4 = 250 / 2 = 125 cups