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The circle with center D is drawn inside the circle with center C, as
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09 Jun 2023, 07:42
09 Jun 2023, 07:42
Expert Reply
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Question Stats:
78% (01:02) correct
21% (01:07) wrong based on 14 sessions
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The circle with center D is drawn inside the circle with center C, as shown in the figure above. If CD = 3, what is the area of semicircle EAB ?
A. \(\frac{9}{2} \pi\)
B. \(9 \pi\)
C. \(12 \pi\)
D. \(18 \pi\)
E. \(36 \pi\)
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Re: The circle with center D is drawn inside the circle with center C, as
[#permalink]
11 Jun 2023, 01:42
11 Jun 2023, 01:42
1
Since CD=3, DE also = 3
Now the radius of the bigger circle is CE= CD+ DE = 3+3 = 6
The area of the bigger circle = π(6)^2 = 36π
So, the area of the halfcircle EAB = 18 π
Ans: D
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Now the radius of the bigger circle is CE= CD+ DE = 3+3 = 6
The area of the bigger circle = π(6)^2 = 36π
So, the area of the halfcircle EAB = 18 π
Ans: D
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Re: The circle with center D is drawn inside the circle with center C, as
[#permalink]
11 Jun 2023, 04:00
11 Jun 2023, 04:00
Expert Reply
OE
The question asks for the area of semicircle EAB. The questions states that the circle with center D has a radius of 3 because CD = 3, which means that the diameter of the smaller circle is equal to 2 × 3 = 6. The radius of the larger circle with center C is the diameter of the smaller circle, which is equal to 6. So, the area of the larger circle is π6 2 = 36π. The area of semicircle EAB is equal to one half the area of the larger circle, so one half of 36π is 18π. The correct answer is (D).
The question asks for the area of semicircle EAB. The questions states that the circle with center D has a radius of 3 because CD = 3, which means that the diameter of the smaller circle is equal to 2 × 3 = 6. The radius of the larger circle with center C is the diameter of the smaller circle, which is equal to 6. So, the area of the larger circle is π6 2 = 36π. The area of semicircle EAB is equal to one half the area of the larger circle, so one half of 36π is 18π. The correct answer is (D).
