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17 Sep 2017, 11:44
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D
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Difficulty:
15%
(low)
Question Stats:
81% (01:25) correct
19%
(01:09)
wrong
based on 60
sessions
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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
17 Sep 2017, 14:01
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SajjadAhmad
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
22 Sep 2017, 11:45
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SajjadAhmad
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
