Bunuel wrote:
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
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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