using the formula SA= 6s2 and V=s3
find the surface area of a room that is 11ft in length, 10 1/2 in width, and 9ft 7inches in height
To find the surface area of the room, we need to calculate the area of each individual side and sum them up.
First, let's convert the given measurements to a single unit. Since the formula for surface area uses the same unit for all sides, we'll convert everything to feet.
Length: 11 ft
Width: 10 1/2 ft = 10.5 ft
Height: Convert 9 ft 7 inches to feet. There are 12 inches in a foot, so 7 inches is 7/12 ft. Adding 9 ft gives us a total height of 9 + 7/12 ft = 9.583 ft (rounded to three decimal places).
Now, we can calculate the area of each side:
1. Top surface: Length * Width
Area = 11 ft * 10.5 ft
2. Bottom surface: Length * Width
Area = 11 ft * 10.5 ft
3. Front surface: Length * Height
Area = 11 ft * 9.583 ft
4. Back surface: Length * Height
Area = 11 ft * 9.583 ft
5. Left side surface: Width * Height
Area = 10.5 ft * 9.583 ft
6. Right side surface: Width * Height
Area = 10.5 ft * 9.583 ft
Now, we can use the surface area formula to calculate the total surface area:
Surface Area (SA) = Area of Top + Area of Bottom + Area of Front + Area of Back + Area of Left Side + Area of Right Side.
SA = (11 ft * 10.5 ft) + (11 ft * 10.5 ft) + (11 ft * 9.583 ft) + (11 ft * 9.583 ft) + (10.5 ft * 9.583 ft) + (10.5 ft * 9.583 ft)
Simply multiply each pair of values, and then add up the results:
SA = 115.5 ft² + 115.5 ft² + 105.413 ft² + 105.413 ft² + 100.1425 ft² + 100.1425 ft²
Finally, add up all these areas to obtain the total surface area:
SA = 641.1115 ft²
Therefore, the surface area of the room is approximately 641.1115 square feet.