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If the area of the circle above is 64π, what is the value of k

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If the area of the circle above is 64π, what is the value of k  [#permalink]

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New post 08 Nov 2018, 05:32
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If the area of the circle above is 64\(π\), what is the value of k ?

(A) 2
(B) 8/3
(C) 4
(D) 16/3
(E) 12

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Re: If the area of the circle above is 64π, what is the value of k  [#permalink]

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New post 08 Nov 2018, 05:58
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HKD1710 wrote:
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If the area of the circle above is \(64π\), what is the value of \(k\) ?

(A) 2
(B) 8/3
(C) 4
(D) 16/3
(E) 12


Project PS Butler : Question #05


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Area of circle \(pi*r^2 = 64\) ---> R = 8


if Radius = 8 then diametr is 16


length of diametre of circle is \(4k-k=16\) ---> \(3k =16\) ---> k =\(\frac{16}{3}\)

IMO: D :)
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Re: If the area of the circle above is 64π, what is the value of k  [#permalink]

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New post 08 Nov 2018, 06:28
\(64*pi = r^2 *pi\)

r = 8

radius = 3k - 1.5k = 1.5k

radius = \(1.5k = \frac{3}{2}* k\)

\(\frac{3}{2} * k = 8\)

\(k = \frac{16}{3}\)

Answer choice D
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Re: If the area of the circle above is 64π, what is the value of k  [#permalink]

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New post 08 Nov 2018, 10:50
As per the given figure.... the diameter of the cicle = \(4k-k=3k\)
Hence, the \(radius(r) = \frac{3k}{2}\)
Thus the area of the circle = \(r^2 * π = 64π\)
or , \(r^2 = 64\)
or , \(r = 8\)
or \(\frac{3k}{2} = 8\)
or \(k =\frac{8*2}{3} = \frac{16}{3}\)............Ans D
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If the area of the circle above is 64π, what is the value of k  [#permalink]

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New post 08 Nov 2018, 10:55
HKD1710 wrote:
As per the given figure.... the diameter of the cicle = \(4k-k=3k\)
Hence, the \(radius(r) = \frac{3k}{2}\)
Thus the area of the circle = \(r^2 * π = 64π\)
or , \(r^2 = 64\)
or , \(r = 8\)
or \(\frac{3k}{2} = 8\)
or \(k =\frac{8*2}{3} = \frac{16}{3}\)............Ans D



HKD1710 why did post solution in the wrong place :lol:
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Re: If the area of the circle above is 64π, what is the value of k  [#permalink]

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New post 08 Nov 2018, 11:30
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dave13 wrote:
HKD1710 wrote:
As per the given figure.... the diameter of the cicle = \(4k-k=3k\)
Hence, the \(radius(r) = \frac{3k}{2}\)
Thus the area of the circle = \(r^2 * π = 64π\)
or , \(r^2 = 64\)
or , \(r = 8\)
or \(\frac{3k}{2} = 8\)
or \(k =\frac{8*2}{3} = \frac{16}{3}\)............Ans D



HKD1710 why did post solution in the wrong place :lol:


Hi dave13,

Someone edited the question by mistake with solution. I have corrected it now. As you can see in the first reply that you only made , that the question was correctly posted. :D
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Re: If the area of the circle above is 64π, what is the value of k  [#permalink]

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New post 08 Nov 2018, 13:22
HKD1710 wrote:
dave13 wrote:
HKD1710 wrote:
As per the given figure.... the diameter of the cicle = \(4k-k=3k\)
Hence, the \(radius(r) = \frac{3k}{2}\)
Thus the area of the circle = \(r^2 * π = 64π\)
or , \(r^2 = 64\)
or , \(r = 8\)
or \(\frac{3k}{2} = 8\)
or \(k =\frac{8*2}{3} = \frac{16}{3}\)............Ans D



HKD1710 why did post solution in the wrong place :lol:


Hi dave13,

Someone edited the question by mistake with solution. I have corrected it now. As you can see in the first reply that you only made , that the question was correctly posted. :D
....... That moron was me ?...... sry for the confusion HKD1710
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Re: If the area of the circle above is 64π, what is the value of k   [#permalink] 08 Nov 2018, 13:22
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