Practice a variety of math problems to keep your math skills at their best. This week, fine-tune your geometry skills by working on the problems below!
E) Cannot be determined
E) No, not based on the information given
This question addresses volumes. Step 1 is to find the volumes of the two vessels.
The rectangle: V = length x width x height
V = 3 x 3.5 x 2
V = 21 feet
Convert feet to inches: V = 252 cubic inches
The cone cup: V = 1/3 π r2
V = 1/3 π 22
V = 20.94 cubic inches
Step 2 is to see how many cups of liquid are needed to fill the container to the max:
Volume of box ÷ Volume of Cone
252 ÷ 20.94
Analysis: If a contestant only pours 12 cups of liquid into the container, the container will not be completely full, especially if they spill any of the liquid. Instead, the contestant needs to go back for that 13th cup of liquid in order to officially fill the container as, after the 12th cup, there are still .0344 cubic inches of the container that needs liquid!