Uncle Toby is making a scale model of the battlefield at Fredericksburg. The area he wants to model measures about 11 mi by 7.5 mi. He plans to put the model on a 3.25 ft by 3.25 square table. On each side of the model he wants to leave at least 3 inches between the model and the table edges. what is the largest scale he can use?
Well, Uncle Toby sure doesn't want any battlefield casualties happening on his tabletop! Let's do some calculations to determine the largest scale he can use.
First, let's convert the measurements to a consistent unit, let's say feet. So, 11 miles is equal to 11 * 5280 = 58080 feet, and 7.5 miles is equal to 7.5 * 5280 = 39600 feet.
Now, let's calculate the available space on the tabletop. Since Uncle Toby wants to leave at least 3 inches between the model and the edges of the table, we subtract twice that from each side of the table. So, the usable length of the table becomes 3.25 ft - 2 * (3 in / 12 ft) = 3.25 ft - 0.5 ft = 2.75 ft.
Therefore, the largest scale Uncle Toby can use is determined by dividing the available space on the tabletop by the size of the modeled area. The scale is given by:
Scale = Usable tabletop length / Modeled area length = 2.75 ft / 58080 ft ≈ 0.0000474
So, Uncle Toby can use a scale of approximately 1:0.0000474. I would suggest Uncle Toby to add some tiny clowns to the model to lighten the mood amidst all that battlefield glory!
To determine the largest scale Uncle Toby can use, we need to consider the dimensions of the model and the available space on the table.
1 mile is equal to 5280 feet, so the model's dimensions are:
Length: 11 miles * 5280 feet/mile = 58080 feet
Width: 7.5 miles * 5280 feet/mile = 39600 feet
According to the given information, the table's dimensions are:
Length: 3.25 feet
Width: 3.25 feet
Uncle Toby wants to leave a 3-inch gap between the model and the table edges on all sides. Since there are 12 inches in a foot, this gap can be converted to feet:
Gap: 3 inches / 12 inches/foot = 0.25 feet
To determine the available space on the table, we subtract the gaps from the table dimensions:
Available length: 3.25 feet - 2 * 0.25 feet = 2.75 feet
Available width: 3.25 feet - 2 * 0.25 feet = 2.75 feet
Now we can calculate the largest scale Uncle Toby can use by dividing the available space on the table by the corresponding dimension of the model:
Largest scale for length = Available length / Model length
Largest scale for width = Available width / Model width
Largest scale for length = 2.75 feet / 58080 feet ≈ 0.0000474
Largest scale for width = 2.75 feet / 39600 feet ≈ 0.00007
Therefore, the largest scale Uncle Toby can use is approximately 0.0000474 (1:21,075) in terms of length, and approximately 0.00007 (1:14,286) in terms of width.
To find the largest scale Uncle Toby can use, we need to consider the dimensions of the model, the dimensions of the table, and the desired gap between the model and the table edges.
Let's start by converting all the measurements to the same units. We'll convert the dimensions of the area he wants to model from miles to feet:
11 miles = 11 * 5280 feet = 58080 feet
7.5 miles = 7.5 * 5280 feet = 39600 feet
Now let's calculate the maximum dimensions of the model to fit on the table. We subtract twice the desired gap from the table dimensions:
Max length = 3.25 feet - 2 * 3 inches = 3.25 feet - 2 * (3/12) feet = 3.25 - 0.5 = 2.75 feet
Max width = 3.25 feet - 2 * 3 inches = 3.25 feet - 2 * (3/12) feet = 3.25 - 0.5 = 2.75 feet
Now we can find the largest scale using the formula:
Scale = Maximum dimension of the model / Corresponding dimension of the area
For the length scale:
Length scale = Max length / Length of the area = 2.75 feet / 58080 feet ≈ 0.0000474
For the width scale:
Width scale = Max width / Width of the area = 2.75 feet / 39600 feet ≈ 0.00007
The largest scale Uncle Toby can use is approximately 0.00007.