In a rectangular room 10 feet wide, 40 feet long and 15 feet high there are four windows, each 30 inches by 48 inches. What is the ratio of window surface to floor area in this room?
4(30*48)/(12*10)(12*40) = ?
To find the ratio of window surface to floor area, we need to calculate the total surface area of the windows and the floor separately.
First, let's calculate the window surface area.
Given:
- Each window measures 30 inches by 48 inches.
To calculate the area of one window, use the formula: area = length × width.
- Area of one window = 30 inches × 48 inches.
Since there are four windows, we multiply the area of one window by 4 to get the total window surface area.
- Total window surface area = 4 × (30 inches × 48 inches).
Next, let's calculate the floor area.
Given:
- The room's width = 10 feet.
- The room's length = 40 feet.
To calculate the area of the floor, use the formula: area = length × width.
- Area of the floor = 10 feet × 40 feet.
Now that we have both the window surface area and the floor area, we can calculate the ratio.
- Ratio = Total window surface area / Area of the floor.
Now let's do the calculations:
Total window surface area = 4 × (30 inches × 48 inches) = 4 × 1440 square inches.
Area of the floor = 10 feet × 40 feet = 400 square feet.
Now, let's convert the window surface area to square feet since the floor area is given in square feet.
- Total window surface area = (4 × 1440 square inches) / (12 inches × 12 inches) square feet.
Finally, let's calculate the ratio:
- Ratio = Total window surface area / Area of the floor = ((4 × 1440 square inches) / (12 inches × 12 inches)) / 400 square feet.
Simplifying further, we find that the ratio of window surface to floor area in this room is:
- Ratio = ((4 × 1440) / (12 × 12)) / 400 = 48 / 400 = 0.12.
Therefore, the ratio of window surface to floor area in this room is 0.12.
To find the ratio of window surface area to floor area, we first need to calculate the surface area of the windows and the floor.
1. Calculate the area of each window:
- The dimensions of each window are given as 30 inches by 48 inches.
- To find the area of each window, we multiply the length and width:
Area of each window = 30 inches * 48 inches.
2. Calculate the total area of all windows:
- Since there are four windows, we need to multiply the area of each window by the number of windows:
Total window surface area = 4 * (Area of each window).
3. Calculate the floor area:
- The dimensions of the room are given as 10 feet by 40 feet.
- To find the floor area, we multiply the length and width:
Floor area = 10 feet * 40 feet.
4. Convert measurements to the same unit:
- Since the dimensions of the windows are in inches and the dimensions of the room are in feet, we need to convert one of them.
- Let's convert the window dimensions to feet by dividing each dimension by 12 (since there are 12 inches in a foot).
5. Final calculations:
- Convert the window dimensions: 30 inches / 12 = 2.5 feet (rounded to one decimal place) and 48 inches / 12 = 4 feet.
- Calculate the area of each window: Area of each window = 2.5 feet * 4 feet.
- Calculate the total window surface area: Total window surface area = 4 * (Area of each window).
- Calculate the floor area: Floor area = 10 feet * 40 feet.
6. Find the ratio:
- Divide the total window surface area by the floor area:
Ratio = Total window surface area / Floor area.
By following these steps, you can now calculate the ratio of window surface to floor area in the given room.