A circular logo is enlarged to fit the lid of a jar. The new diameter is 50 per cent larger than the original.

Question

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?

A. 50
B. 80
C. 100
D. 125
E. 250

Answer 1

The area goes up as the square of the diameter, so the new area is (1.5)^2 times the old area, = 2.25 times larger.

But the question is about the increase. The increase is 125% (the increase is 1.25 units, the 2.25 units less the original 1.0 units)

Answer 2

Circular Logo

Answer 3

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*9/4*(Do)^2

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.

Answer 4

D. 125

If the old area was one, the new area is 1.5*1.5 = 2.25
That is and increase of 2.25 - 1 = 1.25 = 125%

Answer 5

A=pi.r²

if new diameter 50 % larger the radius is the same
r=1.5 ro

A/Ao =(pi.r² ) / (pi.ro²)
A/Ao =(pi.(1.5ro)² ) / (pi.ro²)
A/Ao =(1.5ro)² / ro²
A/Ao =(1.5)²ro² / ro²
A/Ao =(1.5)²
A/Ao =2.25
A=2.25 Ao

So the answer is D the area increased by 125%
Its meaning from 1 to 2.25

Answer 6

Original area = A1 = π (d1)² / 4

New area = A2 = (πd2)² / 4

A2/A1 = d2² / d1² = (1.5)² d1² / d1² = 2.25

A2 = 2.25 A1

Increase = 2.25A1 - 1A1 = 1.25A1

This is an increase of 125%

Answer D

Answer 7

well done.