Toby is making a scale model of the battlefield at Fredericksburg. The area he wants to model measures about 11 mi by 7.5mi. He plans to put the model on a 3.25 ft by 3.25ft 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? I need help!!! Please help me!!!! Thanks!!!
To determine the largest scale Toby can use, we need to calculate the dimensions of the model itself, taking into account the desired spacing around the edges.
First, convert the dimensions of the model and the table to the same unit of measurement. Let's use inches for consistency.
The area Toby wants to model measures 11 mi by 7.5 mi, which is equivalent to:
11 mi * 5280 ft/mi * 12 in/ft = 696,960 inches by
7.5 mi * 5280 ft/mi * 12 in/ft = 475,200 inches.
The table measures 3.25 ft by 3.25 ft, which is equivalent to:
3.25 ft * 12 in/ft = 39 inches by
3.25 ft * 12 in/ft = 39 inches.
Toby wants to leave at least 3 inches of space between the model and the table edges on each side. Therefore, the dimensions of the model itself would be:
(696,960 inches - 3 inches - 3 inches) by (475,200 inches - 3 inches - 3 inches).
Calculating the dimensions of the model, we have:
(696,960 inches - 6 inches) by (475,200 inches - 6 inches) =
696,954 inches by 475,194 inches.
To find the largest scale Toby can use, divide the dimension of the model (696,954 inches) by the dimension of the table (39 inches):
696,954 inches ÷ 39 inches = 17,868.10.
Therefore, the largest scale Toby can use is approximately 17,868.
Note: Since scales are typically expressed as whole numbers, Toby may opt to round down the scale to a whole number, such as 17,000 or 17,500, for practical purposes.
To find the largest scale Toby can use, we need to determine the dimensions of the model on the table and then calculate the scale factor.
First, let's calculate the dimensions of the model on the table:
- The width of the model on the table will be 3.25 ft - (2 * 3 inches).
- 2 * 3 inches accounts for leaving a 3-inch gap on each side of the model.
- Convert inches to feet: 3 inches = 3/12 ft = 0.25 ft.
- Subtracting twice the 0.25 ft gives us: 3.25 ft - 0.5 ft = 2.75 ft.
- The length of the model on the table follows the same calculation, so it's also 2.75 ft.
Now, let's find the scale factor by comparing the dimensions of the model on the table to the actual dimensions of the battlefield:
- Divide the width of the model on the table by the actual width of the battlefield: 2.75 ft / 11 mi.
- Convert the miles to feet: 11 mi * 5280 ft/mi = 58080 ft.
- Calculate the scale factor for the width: 2.75 ft / 58080 ft ≈ 0.0000474.
- Repeat the same calculation for the length of the model: 2.75 ft / 7.5 mi * 5280 ft/mi ≈ 0.00218.
Now, we have two scale factors for the width and length. We need to choose the smaller scale factor to ensure that the model fits on the table.
Therefore, the largest scale Toby can use is approximately 0.0000474.
calm down, and take things one step at a time.
the model is 3.25 ft on a side. That's 39 inches.
a 3" border all around leaves 33" on a side for modeling.
The largest dimension (11 mi) must fit into 33 inches. That's 11mi/33in = 1/3 mi/in, or 1760 ft/in