The model of a new apartment building is 10 in, x 28 in x 18 in. the architect plans for the new building to be 144 times the size of the model. What will the volume and surface area of the new building be when it is completed?
10 x 18 x 28 = 5040 x 144^3 divided by 12 =1254113280ft, but the answer is 8,709,120 ft^3, and i don't understand how they got it, didn't even get to surface area
you need to divide by 12^3 to get it into feet^3, not divide by 12.
volume=5040*144^3(1/12^3)=5040(12^3)
How do you get the surface area?
To calculate the volume of the new building, you need to multiply the dimensions of the model by 144, not by 144^3. Here's the correct calculation:
10 in x 18 in x 28 in = 5040 in^3 (volume of the model)
5040 in^3 x 144 = 725,760 in^3 (volume of the new building)
To convert the volume to ft^3, you need to divide by 12^3 (since there are 12 inches in a foot):
725,760 in^3 ÷ (12 in/ft)^3 = 725,760 ÷ 1728 = 420 ft^3
Therefore, the correct volume of the new building is 420 ft^3, not 8,709,120 ft^3.
Regarding the surface area, we need more information about the shape and layout of the building to accurately calculate it. Can you provide any additional details?
To calculate the volume of the new building, we need to find the volume of the model and then multiply it by 144. The model's volume is given by its dimensions: 10 inches x 28 inches x 18 inches.
To convert the dimensions from inches to feet, we divide each by 12 (since there are 12 inches in a foot):
10 inches / 12 = 0.8333 feet
28 inches / 12 = 2.3333 feet
18 inches / 12 = 1.5 feet
So, the model's dimensions in feet are approximately 0.8333 ft x 2.3333 ft x 1.5 ft.
Now, to find the volume, we multiply the dimensions:
Volume of the model = 0.8333 ft x 2.3333 ft x 1.5 ft = 2.5833 ft^3
Next, we multiply the volume of the model by 144 to get the volume of the new building:
Volume of the new building = 2.5833 ft^3 x 144 = 372.6667 ft^3
Therefore, the volume of the new building, when completed, is approximately 372.6667 ft^3, not 8,709,120 ft^3 as mentioned in the question.
Now, as for the surface area, we need to know the dimensions of each side of the building's exterior walls in order to calculate it. If you provide those dimensions, I can help you determine the surface area.