Different Area

The area of a circle is pi times the radius squared.

As pi will be in the area formula for all the shapes, this can be omitted (cancelled out). Thus, we have to find the circles with a different value for r^2.

A) $1^{2}$ =1,

B) $0.5^{2} \times 4$ =1,

D) $2^{2} \times0.25$ =1,

However,

C) $1.5^{2} \times0.5$ =1.125

Thus, the area of shape C is different

Python 2.7:

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from math import pi
def area(num_circles, diameter):
    return num_circles * pi*(diameter/2.0)**2
letters = "ABCD"
# pairs indicate number of circles and their diameter
circles = ((1, 2), (4, 1), (0.5, 3), (0.25, 4))
areas = []
for num_circles, diameter in circles:
    areas.append(area(num_circles, diameter))
common = None
found = set()
for area in areas:
    if area not in found:
        found.add(area)
    else:
        common = area
        break
for index in xrange(len(areas)):
    if areas[index] != common:
        print "Answer:", letters[index]
        break

Another way to think of this question is which number given is different? A semicircle of radius 3 is an odd numbered radius. If I square the radius (following the formula for area of a circle), I get an odd number (9). Then because it's a semicircle, its area is half that number times pi. This yields a decimal number for the area.

When you look at the other choices, they all deal with either even numbers or 1. 1 has a special property that anything multiplied by 1 will be unchanged, meaning that 1^2 is still 1 and when an even number is multiplied by 1, it will remain an even number. Also, a whole number will remain a whole number when multiplied by 1.

With this knowledge in mind, we can discern quite easily that none of the other areas will be a decimal number multiplied by pi. Therefore due to the question's parameters, the shape with the different area (if there is one, which there is) must be C, a semicircle of radius 3.

One final way to think about it is do two choices have the same area with another having a different area? If yes, then we need not bother worrying about the fourth choice, as the answer will be the choice with the different area.

C has the area of 3.53 rest are having 3.14

Area of a circle = pi.r^2

Area of a circle with diameter 2 = pi.1^2 = pi

Area of 4 circles with diameter 1= 4.pi.0,5^2=pi

Area of quarter circle with Diameter 4 = 1/4.pi.2^2=pi

Area of semicircle with diameter 3 = 1/2.pi.1,5^2= 1,125.pi

in a),b),d)area=1 * (pie)

and

c)having area=1.125 * (pie)

The other three are red, blue, and yellow, which are primary colors. C is green, which is not a primary color, so it is different.

Furthermore, A, B, and D can fit inside a square with side length 2 while C cannot.

Also, A is 1 circle and $\sqrt{1}=1$ , B is 4 circles and $\sqrt{4}=2$ , C is half a circle and $\sqrt{1/2}$ is not rational, and D is 1/4 of a circle and $\sqrt{1/4}=1/2$ . Clearly C is the odd one out.

Finally, A, B, and D all have area $\pi$ while C does not.

We knew area of circle is pie r square A) diameter is 2 thus radius is 1 . 1 square =1 B) diameter is 1 thus radius is 1/2 . 1/2 square is 1/4 *4 = 1 D) diameter is 4 thus radius is 2 and . 2 square is 4 *0.25 = 1 Where as C) diameter is 3 thus radius is 1.5 . 1.5 square * 0.25 = 1.125 Thus C) is different....

Pi x r squared. 1x1=1, .5x.5x4=1, 1.5x1.5/2=1.125, 2x2x.25=1 C is wrong answer.

Applying the basic rule for area we know that area of a circle is pi times the radius squared while that of a semi circle is jalf of pi tomes the radius squared and like so As pi will be in the area formula for all the shapes, this can be omitted (cancelled out). Thus, we have to find the circles with a different value for r^2. A) =1, B) =1, D) =1, However, C) =1.125 Hence C is the odd one out

Except semicircle ,each is having area pie(3.14) using formula of area of circle

Area of a circle is Pi r2, thus C equals 3.534 while A, B and C equals 3.141

A= 2pi R^2= 2pi

B= 4(2pi 1/2^2)= 2pi

C= 1/2 (2pi 3/2^2)= 9/4 pi

D= 1/4 ( 2pi 4/2^2)= 2 pi

We calculate areaof each,which by putting radius values in pi r2 is 3.14 in cases a ,b and d therefore figure 3 is different than others.ans

Just look at the diameters of all options, C is an oddball. So my thinking is that let's forget about the exact formula of calculating the area of a circle, the area of a circle has to do with its diameter, that is all we need to know. Comparing A to B, the diameter was halved (from 2 to 1), but the number of circles are quadrupled, so that should negate each other. Comparing A to D, the diameter was doubled (from 2 to 4), but the D was sliced into a quarter of a cirlcle, so that should negate each other too. In other words, between A to B and between A to D, it is a balanced play between the differences of diameters and whethe the number of circles is either multiplied by four (A to B) or divided by 4 (A to D). So that makes A, B, D the same in size. That leaves the option C, which has a diameter of 3, not a multiplication of 2 by any means. It has to be the oddball.

Ans C as π(1.5)^2÷2=3.5

A,B& D area are π, and c area is 1.125π. so c is different to others.

A) 2 x 2 x pi = 4 x pi.

B) 4 x 1x 1 x pi = 4 x pi.

C) 3 x 3 x pi x 1/2 = 9/2 x pi.

D) 4 x 4 x pi x 1/4 = 4 x pi.

=> The answer is C