Problem Solving

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

OA is B.

I am getting option A as answer .. But how B?


Please let me know

Thanks
Senthil

(22/7)*(7/16)*(7/16)*(2)*(2)

Try again..its B.

First, let's figure out the radius of the pond, in miles rather than inches.

We know that the radius is 7/16 of 2 miles = 14/16 of one mile (7/16 * 2) = 7/8 of a mile.

Now, we need to find the area of the pond, which is easy enough to do using pi * radius squared.

Radius squared is (7/8)*(7/8) = 49/64. Now we must multiply that by pi, which we can just call 3 for estimating purposes.

In fact, we can estimate even more. Let's call the area 50/60 rather than 49/64 (we're estimating, it will be close enough).

(50/60)*3 = 150/60 = 2.5, pretty close to the right answer, B.

Hope this helps!