The area of a square floor on a scale drawing is 36 square centimeters, and the scale drawing is 1 centimeter: 5 ft. What is the area of the actual floor? What is the ratio of the area in the drawing to the actual area?
incorrect answer
well, say it was 6 cm by 6cm
6 * 5 ft/cm * 6 * 5 ft/cm = 36 times 25 ft^2
when you area do scale ratio squared
when you do volume use scale ratio cubed
scale: 1cm = 5ft.
1cm^2 = 25ft.^2.
1. A = 36cm^2 * 25ft^2/cm^2 = 900 sq. ft.
2. Ratio = 36/900 =
To find the area of the actual floor, we need to convert the scale from centimeters to feet. We can start by finding the conversion factor.
Given that the scale drawing is 1 centimeter: 5 feet, this means that 1 centimeter on the drawing represents 5 feet in real life.
To convert the area, we need to square the conversion factor. So, 1 centimeter is equivalent to (5 feet)^2, or 25 square feet.
Now, let's find the area of the actual floor. We know that the area of the square floor on the scale drawing is 36 square centimeters.
Since the area of a square is given by the formula length x width, and all sides of a square are equal, we can find the length of one side of the square by taking the square root of the area.
√36 = 6 centimeters
Now, let's convert the side length from centimeters to feet using the conversion factor we found earlier.
6 centimeters x 5 feet/1 centimeter = 30 feet
Since all sides of a square are equal, the area of the actual floor is given by the formula side length x side length. Therefore, the area of the actual floor is:
30 feet x 30 feet = 900 square feet
To find the ratio of the area in the drawing to the actual area, we divide the area of the drawing by the area of the actual floor:
36 square centimeters / 900 square feet
We need to convert the units to be consistent. Since 1 square foot is equivalent to 929.0304 square centimeters, we can convert the area of the actual floor to square centimeters:
900 square feet x 929.0304 square centimeters/1 square foot = 836127.36 square centimeters
Now, the ratio is:
36 square centimeters / 836127.36 square centimeters ≈ 1/23170.76
Therefore, the ratio of the area in the drawing to the actual area is approximately 1:23170.76.