Final answer:
The scale factor between the actual classroom floor and the scale drawing is 1/48. Using this scale factor, the width in the scale drawing is found to be 8 inches. Thus, the area of the classroom floor in the scale drawing is 72 square inches.
Step-by-step explanation:
The student's question asks for the area of the floor in the scale drawings, given that the actual dimensions of the floor are 36 feet in length and 32 feet in width, and the scale drawing has a length of 9 inches. To solve this, we first need to figure out the scale factor between the actual size and the scale drawing.
To find the scale factor, we compare the actual length to the scale drawing length:
- Actual length: 36 feet
- Scale drawing length: 9 inches
Since there are 12 inches in a foot, the actual length in inches is 36 feet x 12 inches/foot = 432 inches. The scale factor is the ratio of the scale drawing to the actual size: 9 inches (scale drawing) / 432 inches (actual) = 1/48.
Now, to find the scaled width, we use the same scale factor:
- Actual width: 32 feet = 384 inches
- Scaled width = Actual width x Scale factor = 384 inches x (1/48) = 8 inches
Now that we have both dimensions in the scale drawing, we can calculate the area in square inches:
- Length in scale drawing = 9 inches
- Width in the scale drawing = 8 inches
- Area in scale drawing = Length x Width = 9 inches x 8 inches = 72 square inches
Therefore, the area of the floor in the scale drawings is 72 square inches.