If a large pizza has a radius that is 30% larger that that of a medium

I. Assign values

Radius and area
Let 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