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A circular lawn with a radius of 5 meters is surrounded by a

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by BTGmoderatorDC » Sun Feb 24, 2019 7:10 am

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A circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide. What is the area of the walkway?

A. 81 π
B. 56 π
C. 25 π
D. 20 π
E. cannot be determined

OA B

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by [email protected] » Sun Feb 24, 2019 11:45 am
Hi All,

We're told that a circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide. We're asked for the area of the walkway. This is an example of a 'punch out' question - we need to find the area of the ENTIRE shape and then 'punch out' the part that we don't want.

The radius of the ENTIRE circle is (5+4) = 9, so the area of the large circle is (R^2)Ï€ = (9^2)Ï€ = 81Ï€
The radius of the lawn is 5, so the area of the small circle is (R^2)Ï€ = (5^2)Ï€ = 25Ï€

The area of the walkway is the total area - the area of the law... 81Ï€ - 25Ï€ = 56Ï€

Final Answer: B

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by swerve » Mon Feb 25, 2019 8:30 am
The radius of the larger circle (Walk are inclusive) = 5 + 4 = 9.
$$A_{Larger}=\pi9^2=81\pi\quad\Rightarrow\quad(1)$$
The radius of the smaller circle = 5.
$$A_{Smaller}=\pi5^2=25\pi\quad\Rightarrow\quad(2)$$
$$A_{walkway}=(1)-(2)=56\pi$$
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by Scott@TargetTestPrep » Wed Feb 27, 2019 9:05 am
BTGmoderatorDC wrote:Image

A circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide. What is the area of the walkway?

A. 81 π
B. 56 π
C. 25 π
D. 20 π
E. cannot be determined

OA B

Source: Manhattan Prep
The entire area of the combined lawn and walkway is π(5+4)^2 = 81π. The area of the lawn only is π(5)^2 = 25π. Thus, the area of the walkway is the difference: 81π - 25π = 56π.

Answer: B

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