A room is 3.4 smoots wide, 7.1 smoots long, and 1.5 smoots high. 28% of the room's walls are windows and doors. Determine the inside wall surface area of a 1/20 scale model of the room. (sq. in)
To determine the inside wall surface area of a 1/20 scale model of the room, first, we need to find the inside wall surface area of the actual room.
Step 1: Calculate the total wall surface area of the room.
The room has four walls, so we need to find the area of each wall and then add them up.
Wall 1: Width x Height = 3.4 smoots x 1.5 smoots = 5.1 square smoots
Wall 2: Length x Height = 7.1 smoots x 1.5 smoots = 10.65 square smoots
Wall 3: Width x Height = 3.4 smoots x 1.5 smoots = 5.1 square smoots
Wall 4: Length x Height = 7.1 smoots x 1.5 smoots = 10.65 square smoots
Total Wall Surface Area = Wall 1 + Wall 2 + Wall 3 + Wall 4
= 5.1 + 10.65 + 5.1 + 10.65
= 31.5 square smoots
Step 2: Calculate the wall area occupied by windows and doors.
Given that 28% of the wall area is windows and doors.
Area of windows and doors = 28% of Total Wall Surface Area
= 0.28 x 31.5 square smoots
= 8.82 square smoots
Step 3: Calculate the inside wall surface area of the actual room.
Inside Wall Surface Area = Total Wall Surface Area - Area of windows and doors
= 31.5 square smoots - 8.82 square smoots
= 22.68 square smoots
Step 4: Calculate the inside wall surface area of the 1/20 scale model.
As the scale is 1/20, we need to multiply the inside wall surface area of the actual room by the square of the scale factor.
Scale Factor = 1/20
Scale Factor^2 = (1/20)^2 = 1/400
Inside Wall Surface Area of the 1/20 scale model = Inside Wall Surface Area x Scale Factor^2
= 22.68 square smoots x 1/400
= 0.0567 square smoots
Step 5: Convert the area to square inches.
Since 1 smoot is equal to 67 inches, we can convert the area to square inches.
Inside Wall Surface Area (sq. in) = Inside Wall Surface Area (square smoots) x (67 inches/smoot)^2
= 0.0567 square smoots x (67 inches)^2
= 0.0567 x 67 x 67 square inches
= 0.0567 x 4489 square inches
≈ 255.02 square inches
Therefore, the inside wall surface area of a 1/20 scale model of the room is approximately 255.02 square inches.
To determine the inside wall surface area of a 1/20 scale model of the room in square inches, we need to calculate the surface area of the room and then scale it down using the given scale.
Step 1: Calculate the surface area of the room:
Since we are given the width, length, and height of the room, we can calculate its surface area using the formula for the surface area of a rectangular prism:
Surface Area = 2 * (length * width + length * height + width * height)
Surface Area = 2 * (7.1 * 3.4 + 7.1 * 1.5 + 3.4 * 1.5)
Surface Area = 2 * (24.14 + 10.65 + 5.1)
Surface Area = 2 * 39.89
Surface Area = 79.78 square smoots
Step 2: Calculate the inside wall surface area of the scaled-down model:
Since the scale of the model is 1/20, we need to divide the surface area of the room by 20 to get the inside wall surface area of the model in square smoots:
Inside Wall Surface Area of Model = Surface Area of Room / (Scale)^2
Inside Wall Surface Area of Model = 79.78 / (20)^2
Inside Wall Surface Area of Model = 79.78 / 400
Inside Wall Surface Area of Model = 0.1994 square smoots
Step 3: Convert square smoots to square inches:
Since the final answer is required in square inches, we need to convert square smoots to square inches. We can use the conversion factor of 1 smoot = 67 inches, which means 1 square smoot is equivalent to (67^2) square inches.
Inside Wall Surface Area of Model (sq. in) = Inside Wall Surface Area of Model (sq. smoots) * (Conversion Factor)^2
Inside Wall Surface Area of Model (sq. in) = 0.1994 * (67^2)
Inside Wall Surface Area of Model (sq. in) ≈ 897.16 square inches
Therefore, the inside wall surface area of a 1/20 scale model of the room is approximately 897.16 square inches.