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505-555 (Easy)|   Geometry|         
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HKD1710
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If the area of the circle above is 64, what is the value of k 08 Nov 2018, 05:32
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D
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81% (01:15) correct 19% (01:15) wrong based on 911 sessions

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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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D
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dave13
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If the area of the circle above is 64, what is the value of k 08 Nov 2018, 05:58
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HKD1710

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



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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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If the area of the circle above is 64, what is the value of k 08 Nov 2018, 06:28
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\(64*pi = r^2 *pi\)

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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If the area of the circle above is 64, what is the value of k 08 Nov 2018, 10:50
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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 64, what is the value of k 08 Nov 2018, 10:55
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HKD1710
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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HKD1710 why did post solution in the wrong place :lol:
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If the area of the circle above is 64, what is the value of k 08 Nov 2018, 11:30
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dave13
HKD1710
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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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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If the area of the circle above is 64, what is the value of k 08 Nov 2018, 13:22
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HKD1710
dave13
HKD1710
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
Show more
....... That moron was me ?...... sry for the confusion HKD1710
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If the area of the circle above is 64, what is the value of k 12 Feb 2020, 12:54
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HKD1710

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
Show more


From the diagram we can see that, 3k = the diameter of the circle
This means 3k/2 = the RADIUS of the circle

Area of circle = \(πr^2\)

Since the radius is 3k/2, and since we are told the area of the circle is 64\(π\), we can write: \(π(\frac{3k}{2})^2 = 64π\)

Evaluate: \(π(\frac{9k^2}{4}) = 64π\)

Divide both sides by \(π\) to get: \(\frac{9k^2}{4} = 64\)

Multiply both sides by 4 to get: \(9k^2 = 256\)

Divide both sides by 9 to get: \(k^2 = \frac{256}{9}\)

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

Answer: D

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Brent
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If the area of the circle above is 64, what is the value of k 01 Sep 2020, 07:59
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Take a look at the line (on the circle) parallel to y-axis. That is the diameter.
So, diameter = 4k-k =3k
radius = 3k/2

Area of circle = (3k/2)^2 = 64pi
Solving the equation will give, k = 16/3
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If the area of the circle above is 64, what is the value of k 01 Sep 2020, 12:39
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HKD1710

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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Diameter of the circle is \(4k - k = 3k\)
Radius of the circle is \(\frac{3k}{2}\)

Now, \(π\frac{3k}{2}\)*\(\frac{3k}{2}=64π\)

Or, \((\frac{3k}{2})^2 = 8^2\)

Hence, \(3k = 16\)

Or, \(k = \frac{16}{3}\), Answer must be (D)
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If the area of the circle above is 64, what is the value of k 27 Jul 2022, 07:13
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HKD1710

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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Area = (pi)r^2
r = 8
d = 16
Vertical diameter is clearly 3k
3k = 16
k = 16/3

Answer choice D.
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If the area of the circle above is 64, what is the value of k 31 Aug 2023, 05:55
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HKD1710

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

Show Spoiler
Attachment:
Q6.JPG
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Pi.r.r = Pi.64
So, r = 8
Diameter = 16
From figure, diameter = 4k-k = 3k

3k = 16
k = 16/3
So, D is the answer.

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