Hello BTG
Having some issues conceptualizing this problem - the best approach.
Could anyone assist?
Thanks in advance
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GMAT Practice exam 2 - Word Problem/geometry
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GMATGuruNY
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Convert the given radius into miles.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
Since 1 inch on the photograph is the equivalent of 2 miles, we get:
(7/16 inches) * (2 miles)/(1 inch) = 7/8 miles.
Area of the pond = πr² ≈ (22/7)(7/8)² = (22*7)/8² = 154/64 = between 2 and 3.
The correct answer is B.
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Radius on the photograph = 7/16 inchlucas211 wrote:Hello BTG
Having some issues conceptualizing this problem - the best approach.
Could anyone assist?
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
Thanks in advance
Actual radius = (7/16)*2 miles = 7/8miles.
Area of the pond = pi*(7/8)^2 = (22/7)*(7/8)*(7/8) = 22*7/64 = 7/3 approximately.
{We can estimate 22/64 as 22/66 = 1/3}
Correct option: B
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Jeff@TargetTestPrep
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We can create a proportion in which n is the radius of the pond in miles:lucas211 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
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
Answer: B
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