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# On an aerial photograph, the surface of a pond appears as

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Bunuel wrote:
mehdiov please post the questions in their original form and provide answer choice with them.

On an aerial photograph, the surface of a pond appears as circular region of radius 7/16 inch. If a distance of 1 inch on the photograph corresponds to an actual distance of 2 miles, which of the following is the closest estimate of the actual surface area of the pond, in square miles?

A. 1.3
B. 2.4
C. 3.0
D. 3.8
E. 5.0

As 1 inch = 2 miles, then 7/16 inches = 2*7/16 = 7/8 miles. So actual radius is 7/8 miles. $$Area=\pi{r^2}\approx{\frac{3.14*49}{64}}\approx{2.4}$$.

thanks. appoligies for that
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Re: On an aerial photograph, the surface of a pond appears as [#permalink]
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Why doesn't converting the area to square inches and then converting from inches to miles work?

$$(\frac{7}{16})^2=\frac{49}{256}$$
$$\frac{49}{256}*\frac{22}{7}=\frac{77}{128}$$
$$\frac{77}{12}*2\approx1.2$$

I chose 1.3 because it's the closest answer, but obviously the conversion to miles needs to happen before calculating the area. Why does this matter, and is there a decent framework to do conversions of this sort that involve squaring and cubing? This seems to pop up often, and I find it slightly confusing. Thanks!

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Re: On an aerial photograph, the surface of a pond appears as [#permalink]
I chose 1.3miles as well but I think they key word here is "square miles". That's the indicator that you need to convert before using the area formula
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Re: On an aerial photograph, the surface of a pond appears as [#permalink]
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mehdiov wrote:
On an aerial photograph, the surface of a pond appears as circular region of radius 7/16 inch. If a distance of 1 inch on the photograph corresponds to an actual distance of 2 miles, which of the following is the closest estimate of the actual surface area of the pond, in square miles?

A. 1.3
B. 2.4
C. 3.0
D. 3.8
E. 5.0

We can create a proportion in which n is the radius of the pond in miles:

1/2 = (7/16)/n

n = 2(7/16)

n = 7/8

Thus, the area of the pond is (7/8)^2 x π. Recall that the fractional approximation of π is 22/7. Thus, we have:

(7/8)^2 x π ≈ 49/64 x 22/7 = 7/32 x 11/1 = 77/32 = 2 13/32 ≈ 2 12/30 = 2 2/5 = 2.4

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Re: On an aerial photograph, the surface of a pond appears as [#permalink]
Did a very silly calculation mistake -> 8*4 = 64
How to avoid such careless mistakes?
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Re: On an aerial photograph, the surface of a pond appears as [#permalink]
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first convert 7/16 inch into miles by multiplying with 2 then find surface are of pond using formula pie r^2
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Re: On an aerial photograph, the surface of a pond appears as [#permalink]
Arent surface area and area different entities? I did 2piR as surface area.
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Re: On an aerial photograph, the surface of a pond appears as [#permalink]

1 inch = 2 miles
1 $$inch^2$$ = 4 $$miles^2$$
7/16 $$inch^2$$ = 7/4 $$miles^2$$

Surface Area = 2πr

So we get 2 x$$\frac{ 22}{7}$$ x $$\frac{7}{4}$$
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Re: On an aerial photograph, the surface of a pond appears as [#permalink]
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Hoozan wrote:
7/16 $$inch^2$$ = 7/4 $$miles^2$$

Firstly, 7/16 is "inch" (not inch^2).

Best way would be to first find the area in terms of inch^2, and then multiple it by 4 to convert the area into miles^2.

Note that the area is pi*r^2 (not 2*pi*r).
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Re: On an aerial photograph, the surface of a pond appears as [#permalink]
EducationAisle wrote:
Hoozan wrote:
7/16 $$inch^2$$ = 7/4 $$miles^2$$

Firstly, 7/16 is "inch" (not inch^2).

Best way would be to first find the area in terms of inch^2, and then multiple it by 4 to convert the area into miles^2.

Note that the area is pi*r^2 (not 2*pi*r).

But isn't the surface area of a circle = 2 x pie x r? And that's what the question has asked us to find right? estimate of the actual surface area of the pond

Also, is it possible for you to show the step-by-step calculation for this question?
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Re: On an aerial photograph, the surface of a pond appears as [#permalink]
As mentined, an easy way would be to first find the area in terms of inch^2, and then multiple it by 4 to convert the area into miles^2.

So, surface area = pi*r^2 = pi*(7/16)^2 inches^2

Surface area = pi*(7/16)^2 * (2^2) miles^2 = 2.4 miles^2
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