An candy store sells boxes of candy bars in large and small boxes. A small box holds 12 candy bars. The large box is formed by doubling the length, widths and height of the small box. About how many candy bars should fit in the large box?
Show work.
(This is 10th grade, please don't make it advanced.)
If a small box holds 12 candy bars, then it has a volume of 12 cubic units.
To find the volume of the large box, we double the length, width, and height of the small box. Let's say the small box has dimensions of 1 unit by 1 unit by 1 unit.
The large box would have dimensions of 2 units by 2 units by 2 units.
The volume of the small box is 1 x 1 x 1 = 1 cubic unit.
The volume of the large box is 2 x 2 x 2 = 8 cubic units.
We can estimate that the large box would hold about 8 times as many candy bars as the small box, since their volumes are directly proportional.
So, about 8 x 12 = 96 candy bars should fit in the large box.
To find out about how many candy bars should fit in the large box, we need to first determine the volume of the large box and then divide it by the volume of a small candy bar.
Step 1: Calculate the volume of a small box.
Since the small box is a rectangular prism, we can calculate its volume using the formula: Volume = length × width × height.
Given:
Length = width = height = 12 (since the small box holds 12 candy bars)
Volume of small box = 12 × 12 × 12 = 1,728 cubic units
Step 2: Calculate the volume of the large box.
According to the given information, the dimensions of the large box are double that of the small box. So, for the large box:
Length = width = height = 12 × 2 = 24
Volume of large box = 24 × 24 × 24 = 13,824 cubic units
Step 3: Find out how many small candy bars can fit in the large box.
To determine the number of small candy bars that can fit in the large box, we need to divide the volume of the large box by the volume of a small candy bar. Since the volume of a small candy bar is not given, we can assume it is 1 cubic unit.
Number of small candy bars that can fit in the large box = Volume of large box / Volume of candy bar
Number of small candy bars that can fit in the large box = 13,824 / 1 = 13,824
Therefore, about 13,824 small candy bars should fit in the large box.