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The figure above shows the inside dimensions in feet of a certain room
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Updated on: 16 Jul 2017, 05:22
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38% (01:02) correct 62% (01:45) wrong based on 627 sessions
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The figure above shows the inside dimensions, in feet, of a certain room. An architect made a scale model of the room that had a floor and four walls, but not a ceiling. What was the scale of the model, in inches per foot, if the inside of the model had a total surface area of 2,304 square inches?
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22 Mar 2017, 20:46
Architect wants to make a model room, so model room dimensions need to be reduced, SO each side needs to be in the same ratio.
let's say on the scale - 1 feet = x inch ( example 10 feet long wall needs to be shown as a model- so we can have a scale of each 1 inch equivalent to= 10 feet, in the same way other dimensions need to be reduced.)
let's say 01 feet = x inch on the scale , NOW WE NEED TO FIND THIS X SO 01 inch = 1/x feet
so area 01 square inch= (1/x)*(1/x) square feet = 1/x^2 we have given the model box area = 2304 square inch so actual area in square feet= 2304 *1/x^2 square feet ------ equation 01
we already have the dimensions of the actual building in feet, let's calculate the are of it -
2*8*10 ( 02 side wall with 8 and 10 feet side) + 2*8*16 + 10*16 ( only the floor, no roof) --------------- equation 2
Re: The figure above shows the inside dimensions in feet of a certain room
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16 Jul 2017, 08:25
good one on scales - the meaning was not clear to me also thanks for the question. i knew the formula for this question... but the application went wrong on my side.. great question any ways,,, thanks
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16 Jul 2017, 12:14
IMO, this question is pretty straight forward since we are looking for in/ft. And that is exactly what the question provided. We already have the scaled surface area in (in sq), i.e 2304 . We just needed to find the original area in feet from the diagram. This is 2(8*10) + 2(16*8) + 16*10 = 576 (ft sq) Scale = 2304 in sq/ 576 ft sq = 4 (in/ft) sq. Take the square root to get 2 in/ft.
Re: The figure above shows the inside dimensions in feet of a certain room
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04 Aug 2017, 12:34
1
I've found these conversion problems particularly confusing, especially because there isn't a well-defined process for handling conversions (at least that I've seen).
Here's a process I've found useful for navigating conversions
Create a conversion ratio:
\(1m : 100cm\)
Raise both sides to the power of the operation (for volume operations, the power is three, for surface are operations, the power is 2, for regular ratios, the power is 1)
So something with a volume of \(15m^3\) is equivalently \(15,000,000cm^3\) in volume
This process can be reversed also. Say, for example, you know the ratio of area for two squares is \(1in^2:16in^2\). This represents a squared amount, so the ratio of these two square's sides is the square root of the ratio of area:
This process is fairly intuitive with base-10 metric conversions, but works the same with questions like this one.
Two \(8x10\) walls:
\(2*8*10 = 160ft^2\)
Two \(8x16\) walls:
\(2*8*16=256ft^2\)
One \(10x16\) wall:
\(10*16=160ft^2\)
So there are \(160+256+160=576ft^2\) of surface area for the actual room, and \(2304in^2\) for the model
\(576ft^2:2304in^2 \rightarrow 1ft^2:4in^2\)
This is a surface area (second dimension) problem with a ratio comparing already squared units, so to find the ratio of the un-squared units (first dimension), take the square root of the ratio:
\(\sqrt{1ft^2}:\sqrt{4in^2} \rightarrow 1ft:2in\)
So for every two inches in the model there is one foot in real life.
Re: The figure above shows the inside dimensions in feet of a certain room
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06 Aug 2018, 07:53
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