A theater decides to change the shape of its popcorn container from a rectangular boc to a right regular pyramid, as shown in the following figure, and charge only half as much. If the containers are the same height and the tops are are the same size, is this a bargain for the customer? explain

No.. the pyramidal shape has 1/3 the volume , while the price was reduced by half it makes

customers pay 50% more for their popcorn

To determine whether this is a bargain for the customer, let's compare the volumes of the rectangular box and the right regular pyramid popcorn containers.

The volume of a rectangular box is calculated by multiplying its length, width, and height. Let's denote the dimensions of the rectangular box as length (L), width (W), and height (H).

The volume of the rectangular box is given by:
Volume_box = L * W * H

On the other hand, the volume of a right regular pyramid is calculated by multiplying its base area and height, and then dividing by 3. Let's denote the dimensions of the base of the pyramid as base length (B) and base width (b), and the height of the pyramid as H (same as the height of the box).

The volume of the right regular pyramid is given by:
Volume_pyramid = (B * b * H) / 3

Given that the tops of the containers are of the same size, we can assume that the base length (B) and base width (b) of the pyramid are the same as the length (L) and width (W) of the box.

So, the volume of the right regular pyramid can be written as:
Volume_pyramid = (L * W * H) / 3

Now, suppose the theater decides to charge only half the price for the pyramid container compared to the box. This means the price is proportional to the volume of the container.

If we compare the volumes of the pyramid and the box, we can see that the volume of the pyramid is one-third of the volume of the box. So, if the price is proportional to volume, then the pyramid container would be charged 1/3 of the price of the box.

Therefore, switching to the right regular pyramid container and charging half the price would actually be a better bargain for the customer, as they would be paying only 1/6th (1/3 * 1/2) of the original price for the same amount of popcorn.

In conclusion, changing the shape of the popcorn container to a right regular pyramid and charging only half the price is a bargain for the customer.

To determine whether this is a bargain for the customer, we can compare the volumes of the rectangular box and the right regular pyramid.

1. Start by finding the volume of the rectangular box. The volume of a rectangular box can be calculated by multiplying its length, width, and height.

2. Next, find the volume of the right regular pyramid. The volume of a right regular pyramid can be calculated by using the formula V = (1/3) * base area * height.

3. Since the tops of the two containers are the same size, the base area of the right regular pyramid is equal to the area of the rectangular box's top face.

4. If the two containers have the same height, you can assume that the height in the volume formulas will be the same, so it can be cancelled out for comparison.

5. Now, compare the volumes of the two containers. If the volume of the right regular pyramid is half or less than half of the volume of the rectangular box, then it is indeed a bargain for the customer.

In summary, to determine if it's a bargain, calculate the volumes of the rectangular box and the right regular pyramid using the formulas provided. Compare the two volumes, and if the volume of the pyramid is half or less than half of the volume of the box, then it is a bargain for the customer.