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If the radius of a circle is decreased by 10%, by what percent is its 08 Mar 2018, 02:18
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85% (00:35) correct 15% (00:38) wrong based on 62 sessions

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If the radius of a circle is decreased by 10%, by what percent is its area decreased?

(A) 10

(B) 19

(C) 21

(D) 79

(E) 81
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If the radius of a circle is decreased by 10%, by what percent is its 08 Mar 2018, 02:18
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Bunuel
If the radius of a circle is decreased by 10%, by what percent is its area decreased?

(A) 10

(B) 19

(C) 21

(D) 79

(E) 81
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23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations



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If the radius of a circle is decreased by 10%, by what percent is its 08 Mar 2018, 02:25
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Bunuel
If the radius of a circle is decreased by 10%, by what percent is its area decreased?

(A) 10

(B) 19

(C) 21

(D) 79

(E) 81
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We'll pick an easy number which can help us make the calculation.
This is an Alternative approach.

Say the original radius was 10. Then the original area is pi*10^2 = 100pi
If the radius decreases by 10% it is now 9. Then the new area is pi*9^2 =81pi
This is a decrease of 100pi - 81pi = 19pi.
Since 19pi 19% of 100pi, our answer is 19%.

(B) is our answer.
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If the radius of a circle is decreased by 10%, by what percent is its 08 Mar 2018, 10:58
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Bunuel
If the radius of a circle is decreased by 10%, by what percent is its area decreased?

(A) 10

(B) 19

(C) 21

(D) 79

(E) 81
Show more
Scale factor:
All changes in dimension of a figure have to do with length. Length is increased or decreased by a scale factor, \(k\)

Decrease in one length only (one dimension) = multiply by \(k\)

Decrease in area?
Area = length*length (two dimensions)
Multiply by \((k*k)= k^2\)

Original area = A
New area = (original area)*(\(k^2\))
(.9)*(.9)*(A) = .81A

Percent decrease: \(\frac{New-Old}{Old}*100\)

\((\frac{-.81A-A}{A}*100) =\frac{|-.19|}{1}*100= 19\) % decrease

Answer B

* Decrease in volume, e.g. cube, if change is uniform = (length * length * length) = multiply by \((k*k*k) = k^3\)
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If the radius of a circle is decreased by 10%, by what percent is its 21 Jul 2020, 10:26
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Bunuel
If the radius of a circle is decreased by 10%, by what percent is its area decreased?

(A) 10

(B) 19

(C) 21

(D) 79

(E) 81
Show more

Area = \pi r^2

Since r' = .9r
New Area = \(\pi r'^2 = \pi .81 r^2 = (1-.19)\pi r^2 \)

IMO B
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