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Area- Aptitude Questions and Answers

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The areas of two circular fields are in the ratio 16 : 49. If the radius of the bigger field is 14 m, then what is the radius of the smaller field?

A)

4 m


B)

8 m


C)

9 m


D)

10 m



Correct Answer :

8 m


Explanation :

Let r1 and r2 be the radius of the circles.
Area of circle = πr2

As is given, Ratio of area πr12/πr22 = 16/49
r12 / r22 = 16 / 49
r1 / r2 = 4 / 7
r1 = (4/7) * 14 ( r2 = 14 m)
r1 = 8 m

If each of the dimensions of a rectangle is increased by 200%, the area is increased by?

A)

300%


B)

400%


C)

600%


D)

800%



Correct Answer :

800%


Explanation :

Let the length and width of the rectangle are x and y respectively.
Then, area of rectangle = xy

Now, Length and Width of rectangle after increasing by 200%
So, New Length = x + (200/100)x = 3x
New Width = y + (200/100)y = 3y

New area = 3x*3y = 9xy

Percentage increase in area = (9xy-xy)*100 / xy = 800 %

A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent in the form of a circle, it encloses an area equal to?

A)

121 cm2


B)

144 cm2


C)

154 cm2


D)

168 cm2



Correct Answer :

154 cm2


Explanation :

As is given, area of square = a2 = 121 cm2
So, side of square, a = 11 cm

length of the wire = Perimeter of square of side a = 4a = 4*11 = 44cm

Let the radius of circle be r cm. Then,
Perimeter of circle = Length of wire
=> 2πr = 44 cm
=> r = 44/2π = 7 (π = 22/7)

Now, Area of circle = πr2 = (22/7) *7*7 = 154 cm2

If the area of a square is 16 cm2, then the area of the square joining the mid-points of the sides is?

A)

32 cm2


B)

8 cm2


C)

4 cm2


D)

16 cm2



Correct Answer :

8 cm2


Explanation :

Area of square, b² = 16 cm²
side of square, b = √16 =4 cm

Diagonal of square inside the big square = Side of big square
√2s = b = 4
s = 2√2 cm

The area of the small square = 2√2 * 2√2 = 4*2 = 8cm²

The area of a triangle is 150 m2 . The ratio of its base to its height is 3:4. Find the length of its base ?

A)

45 cm


B)

30 cm


C)

15 cm


D)

10 cm



Correct Answer :

15 cm


Explanation :

Let the base and height be 3x & 4x.
Area of triangle = 1/2 × Base × Height
150 = 1/2 × 3x × 4x
x = 5

Hence the length of the base is 15 cm.

Relevant links

Area and Perimeter - Important Formulas,Tricks and Examples

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