Bunuel wrote:
If a large pizza has a radius that is 30% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?
A. 30
B. 36
C. 60
D. 69
E. 90
I. Assign valuesRadius and areaLet radius of medium pizza, \(r=10\)
AREA of medium pizza: \(a=πr^2=100π\)
Radius of large pizza, \(R=(10*1.3)=13\)
OR
\(R=(r+.30r)=1.3r=(1.3*10)=13\)
AREA of large pizza, \(A=(π* 13^2)=169π\)
[Percent increase, mental math: 169 is 69% greater than 100 - Answer D]
Percent increase in area = percent change
Percent change: \(\frac{Change}{Original}*100\)
Change: \((169π-100π)=69π\)
Original (area of medium pizza) = \(100π\)
Percent increase in area:
\((\frac{69π}{100π})*100=(.69*100)=69\) %
Answer D
II. Shortcut formula for overall percent change
We have successive percent changes because the radius increases by 30% TWICE
(\(r*r*π\)) => \((R*R*π)\)
SHORTCUT formula
Overall percent change for two successive percent changes:
\(A+B+\frac{A*B}{100}\) percent
\(A\) = first percent change
\(B\) = second percent change
\(30+30+\frac{30*30}{100}\)
\((60+\frac{900}{100})=(60+9)=69\) percent increase
Answer D
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