Answered

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 percentage has the area of the logo increased?

A50
B80
C100
D125
E250

Verified 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=3/2Do

Ao=pi/4(Do)^2
Af=pi/4(Df)^2=pi/4(3/2Do)^2=pi/49/...

Comparing the initial and final area:

Af/Ao=(pi/49/4(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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