A small steel spoon is 6 inches long and weighs approximately 4 ounces. If it is used as a model for a large steel spoon to be constructed from melting approximately 200 lb of steel spoons, how long will the large spoon be?

Question

Quizplus · Accepted Answer

The volume of the large spoon is proportional to the cube of its length, and since weight is proportional to volume for the same material, the relationship between the lengths of the spoons can be found using the cube root of the ratio of their weights. The large spoon is made from 200 lb of steel, which is 3200 ounces (since there are 16 ounces in a pound). The ratio of the weights is 3200 ounces / 4 ounces = 800. The cube root of 800 gives the ratio of the lengths, which is approximately 9.283 (since the cube root of 800 ≈ 9.283). Therefore, the length of the large spoon is 9.283 times the length of the small spoon, which is 6 inches. Converting 9.283 * 6 inches to feet (since 12 inches = 1 foot) gives approximately 55.7 inches, or approximately 4.6 feet.

A Small Steel Spoon Is 6 Inches Long and Weighs