Problem Solving

On an aerial photograph, the surface of a pond appears as circular region of radius 16/7 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

I think you got the question wrong. With those numbers none of the answers make sense. Instead of 16/7 inches i think it should be 7/16 inches.... In which case the answer is 2.4.

7/16 inches * 2 miles/inch = 14/16 = 7/8.

Now:
Pi*( 7/8 )^2 = ~3*(49/64)= ~ 150/64 = ~75/32 or somewhere around 2.5, but we know it's less than 3 and greater than 2.

The only answer that fits is B... 2.4.

mav,

With the numbers you posted I am getting 2.9, which is about 3.0. Let us know the OA.

Actually, if you use the numbers he posted you get ~60.

16/7 inches * 2 miles/inch = 32/7 miles

The surface area in square miles will be: pi(32/7)^2

which is pi(1024/49) or about 3000/50 = ~60

If you use a calculator and a few digits of pi, you get around 65.6.

AleksandrM wrote:mav,

With the numbers you posted I am getting 2.9, which is about 3.0. Let us know the OA.

1 inch = 2 miles

16/7 inch = 32/7 miles

area = pi*32/7*32/7 = 65.67

Are you sure the question is correct?

one needs to convert inches to miles and then square it. we get 2.4 approx with that.

and its 7/16 and not 16/7.

hey everyone !!!
isn't the surface area be ( 2 pie r ) which is equal to approx 5 : answer choice (e)

Wrong question, don't try to solve!
You never get the answer anywhere near the options.