Final answer:
The length of George Washington's nose on the sculpture at Mount Rushmore is approximately 6.8 feet, based on the understanding of proportions and scaling.
Step-by-step explanation:
The question asks us to calculate the length of George Washington's nose on the sculpture at Mount Rushmore if the sculpture's head is approximately 34 feet in height and the actual length of his nose is stated to be 2 inches. To solve this problem, we need to understand proportions and scaling.
Let's assume that the actual height of George Washington's head is proportional to the height of the sculpture's head, and similarly, the actual length of his nose is proportional to the nose on the sculpture.
First, convert the nose length from inches to feet:
1 inch = 1/12 foot2 inches = 2/12 feet = 1/6 feet
Next, we calculate the scale factor which is the ratio of sculpture's head to the actual head size. Assuming the actual size of Washington's head to be around 9 to 10 inches (a common adult head size), we use 10 inches for simplicity.
1 inch = 1/12 foot, thus 10 inches = 10/12 feet = 5/6 feet
Scale Factor = Size of Sculpture's Head / Actual Head Size = 34 feet / (5/6 feet)
Scale Factor = 204/5 = 40.8
Now, let's apply the scale factor to the actual nose size to get the sculpture's nose size.
Length of Sculpture's Nose = Actual Nose Length * Scale Factor = (1/6 feet) * 40.8 ≈ 6.8 feet
Therefore, the nose on the sculpture at Mount Rushmore is approximately 6.8 feet long.