The figure above shows the inside dimensions in feet of a certain room

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)

\((1m)^3:(100cm)^3 \rightarrow 1m^3:1,000,000cm^3\)

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:

\(\sqrt{1in^2}:\sqrt{16in^2} \rightarrow 1in:4in\)

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.

Answer D

So the dimension of the original room is: 576 ft2. (Surface area - ceiling)
The dimension of the model : 2304 in2.

Scale ratio: 2304 in2/576 ft2 = 4 inc2/ft2 => 2 in/ft (ans)

Hi,

Scale is basically the ratio of sides..
Mostly used in MAPs/Sketches

\(Surface\; area:\; the\; area\; of\; all\; surfaces\; inside\; the\; model\;\)

\(\left( remember\; we\; are\; told\; that\; measure\; is\; in\; in^{2},\; so\; it\; can\; only\; be\; a\; sum\; of\; in^{2 \right)\)

\(So\; let\)'\(s\; say\; that\; the\; scale\; is\; represented\; by\; n,\;\)

\(meaning\; that\; if\; the\; real\; deal\; is\; 2*small\; face\; +\; 2*big\; face\; +\; base\; =\; 2*\left( 8*10 \right)+2*\left( 16*8 \right)+10*16\)

\(then\; the\; model\; will\; be\; 2*\left( 8n*10n \right)+2*\left( 16n*8n \right)+10n*16n,\;\)

\(since\; we\; are\; given\; the\; area\; of\; the\; model,\;\)
\(we\; know\; that\; 2*\left( 8n*10n \right)+2*\left( 16n*8n \right)+10n*16n=2304,\; 160n^{2}\; +\; 256n^{2}+160n^{2}=2304,\; 576n^{2}=2304,\)

\(and\; since\; 576\; =\; 625-49\; =\; \left( 25-7 \right)\left( 25+7 \right)\; and\; 2304=\; 2500-196\; =\; \left( 50-14 \right)\left( 50+14 \right),\; \\
n^{2}=\; \frac{\left( 36\cdot 64 \right)}{\left( 18\cdot 32 \right)}\; =\; 4,\;\)

\(n=2\)

\(Answer\; D\)

Quick Question..
Can somebody tell me what does scale refer to here ?
bit confusing
thanks

Scale means- how many times bigger or smaller was the model as compared to the original.

hey
How did you write this =>
"SO if 1 sq feet is represented by 4 square inches..
1 feet will be reprsented by 2 inches"

I guess Gmat will give us the conversion rate ?

I cannot see the full picture. Please fix the error for this post, thanks.

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.

Total surface area = 10*16 + 2 (10+16)*8 = 160 + 416 = 576 sq ft = 2304 sq inch
inch / ft = 2304/576 = 4 inch/ft

IMO E

NO.

the above relation was :

feet^2 =4 inch^2 or value = 4 (inch^2/feet^2)

you need to find

feet =inch or answer = sqrt 4 (inch^2/feet^2) =2 inch/feet

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

equation 2= equation1

8 ( 20 +32+20 ) = 2304/x^2

or x^2 = 2304/8*72

x^2= 4
so x=2

answer D

_______________
Fixed it.

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

chetan2u if they asked instead for the scale of the house to the model in inches per foot then we would have to convert (*12 twice?) the 576 ft ^2 right? But since they ask for inches/per for which is already the units we have there is no need? I misunderstood the question and got mixed up in trying to convert...

Another really hard question off Exam 6. I was paralyzed when I realized I was stumped. Fortunately, you can quickly cross off all numbers but 1.8 and 2. 2 is the obvious one to test first, and it works.

Scale drawing is a drawing which has been reduced or enlarged from its original size, to a specified scale.
The scale is a ratio of the size of the drawing to the size of the original object being drawn.

\(Scale (or scale ratio)= \frac{the size of the drawing}{size of the original object being drawn}\\
\)

\(Area of the original Object = 2*(8*10) + 2*(16*8)+(16*10) = 576 feet^2\)

\(Area of scale model= 2304 inch^2\)

\(Scale= \frac{2304 inch^2}{ 576 feet^2}\)
=\( \frac{4 inch^2}{feet^2}\)
i.e. 4 square inch in drawing represents 1 square foot in real life
the question says to find scale in \(\frac{inch}{feet}\), so 2 inch represent 1 square foot.