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Circle P is inside Circle Q, and the two circles share the same center
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17 Sep 2017, 11:44
17 Sep 2017, 11:44
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Circle P is inside Circle Q, and the two circles share the same center X. If the circumference of Q is four times the circumference of P, and the radius of Circle P is three, what is the difference between Circle Q’s diameter and Circle P’s diameter?
A 6
B 9
C 12
D 18
E 24
A 6
B 9
C 12
D 18
E 24
Circle P is inside Circle Q, and the two circles share the same center
[#permalink]
17 Sep 2017, 14:01
17 Sep 2017, 14:01
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SajjadAhmad wrote:
Circle P is inside Circle Q, and the two circles share the same center X. If the circumference of Q is four times the circumference of P, and the radius of Circle P is three, what is the difference between Circle Q’s diameter and Circle P’s diameter?
A 6
B 9
C 12
D 18
E 24
A 6
B 9
C 12
D 18
E 24
This question requires us to find the diameter of larger Circle Q.
Circle P's radius is given. From that derive P's diameter and circumference, then Q's circumference and diameter.
Circle P radius = 3, so
P's diameter is \(2r = 6\)
P's circumference is \(\pi*d\)
P's circumference = \(6\pi\)
Circle Q's circumference is four times that of P.
Q's circumference: \(6\pi * 4 = 24\pi\)
Circle Q's diameter is derived from its circumference:
Q's circumference:
\(24\pi = \pi*d\)
Q's diameter, \(d = 24\)
P's diameter, \(d = 6\)
The difference between the two diameters is (24 - 6) = 18
ANSWER D
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Re: Circle P is inside Circle Q, and the two circles share the same center
[#permalink]
22 Sep 2017, 11:45
22 Sep 2017, 11:45
1
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Expert Reply
SajjadAhmad wrote:
Circle P is inside Circle Q, and the two circles share the same center X. If the circumference of Q is four times the circumference of P, and the radius of Circle P is three, what is the difference between Circle Q’s diameter and Circle P’s diameter?
A 6
B 9
C 12
D 18
E 24
A 6
B 9
C 12
D 18
E 24
Since the radius of Circle P (the smaller circle) is 3, the diameter and circumference of Circle P are 6 and 6π, respectively. Since the circumference of Circle Q is four times the circumference of Circle P, the circumference and diameter of Circle Q are 24π and 24, respectively.
Thus, the difference between the diameters of Circles Q and P is 24 - 6 = 18.
Answer: D
