A circular logo is enlarged to fit the lid of a jar. The new diameter is 50 per cent larger than the original. By what percentag
e has the area of the logo increased?
a. 50
b. 80
c. 100
d. 125
e. 250
1 answer:
It is easier to show th anser using fractions.
Do=original diameter
Ao=Original area
Df=Final diameter
Af=Final area
Df=(1+50%)Do=(1+1/2)Do=3/2*Do
Ao=pi/4*(Do)^2
Af=pi/4*(Df)^2=pi/4*(3/2*Do)^2=pi/4*9/...
Comparing the initial and final area:
Af/Ao=(pi/4*9/4*(Do)^2)/(pi/4*(Do)^2)
simplifying
Af/Ao=9/4=225%
Therefore the increment is 9/4-1=5/4=125%
Or equivalently: 225%-100%=125%
Therefore the answer is "D."
Note: there is calculate the increment in the difference not how many times the area changed.
Hope this helps ;)
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