Final answer:
A replica of the Lombardi Trophy at triple the original size would require 27 times more silver, resulting in a weight of 180.9 pounds.
Step-by-step explanation:
The student is asking about scaling dimensions and the corresponding increase in mass when the size of an object is increased. If Tiffany and Co. wanted to create a replica of the Lombardi Trophy that is triple the size of the original, it is important to understand that tripling the linear dimensions (height, width, and depth) of a three-dimensional object would actually increase its volume, and therefore mass, by a factor of 33, or 27 times. Since the original trophy is made of 6.7 pounds of silver, the replica would require 27 times more silver. Therefore, to calculate the amount of silver needed for the replica trophy, we multiply 6.7 pounds by 27.
6.7 pounds x 27 = 180.9 pounds
So, the replica would be made of 180.9 pounds of silver.
To find the amount of silver needed to create a replica triple the size of the original Lombardi Trophy, we can use the concept of ratios. Since the height of the original trophy is 20.75 inches and the weight of silver used is 6.7 pounds, we can set up a ratio.
Ratio of height: original height : replica height = 20.75 inches : x inches
Ratio of weight: original weight : replica weight = 6.7 pounds : y pounds
Since the replica is triple the size, the ratios can be set up as:
Ratio of height: 20.75 inches : 3 * 20.75 inches = 1 : 3
Ratio of weight: 6.7 pounds : 3 * 6.7 pounds = 1 : 3
Using these ratios, we can find the replica weight by multiplying the original weight by 3:
Replica weight = 6.7 pounds * 3 = 20.1 pounds