b The cylindrical container gives more popcorn for your money. See solution.
Practice makes perfect
a Let's analyze the two containers for popcorn: one a cone and one a cylinder.
Notice that the radii and heights of the containers are both the same. We are asked how many small containers of popcorn you have to buy to equal the amount of popcorn in a large container. To answer the question, let's analyze the formulas for the volume of a cone and for the volume of a cylinder.
Volume of Cone: 1/3π r^2h Volume of Cylinder: π r^2h
Notice that the volume of the cone is three times smaller than the volume of the cylinder. Therefore, we have to buy three small, cone-shaped containers to equal the amount of popcorn in the large container.
b Popcorn in a small container costs $1.25 and popcorn in a big container costs $2.50. This tells us that we can get one big order or two small orders for $2.50.
$2.5= c One Big Order =
c Two Small Orders
From Part A we know that the volume of three small containers equals to the volume of the big one. Therefore, getting two small orders will get us less popcorn than getting one big order, but we spend the same amount of money. This tells us that the big container gives you more popcorn for your money.
