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121. If radius of a circle is increased by 5%, find the precentage increase in its area.
  A.  12.85%
  B.  11.75%
  C.  8.50%
  D.  10.25%
     
   
View Answer

Shortcut:
If all the measuring sides of any two dimensional figure is changed by a%, then its area changes by
(
2a +
a2 / 100
)
%
Here, a = 5
Required percentage =
(
2 x 5 +
52 / 100
)
%
=
(
10 +
25 / 100
)
% = 10 + 0.25= 10.25%

122. If all the sides of a hexagon is increased by 2%, find the percentage increase in its area.
  A.  4.80%
  B.  6.20%
  C.  4.04%
  D.  5.14%
     
   
View Answer

Shortcut:
If all the measuring sides of any two dimensional figure is changed by a%, then its area changes by
(
2a +
a2 / 100
)
%
Here, a = 2
Required percentage =
(
2 x 2 +
22 / 100
)
%
=
(
4 +
4 / 100
)
% = 4 + 0.04 = 4.04%

123. Of the two square fields, the area of one is 1 hectare, while the other one is broader by 1%. The difference in areas is:
  A.  198 sq m
  B.  201 sq m
  C.  211 sq m
  D.  207 sq m
     
   
View Answer

Shortcut:
If all the measuring sides of any two dimensional figure is changed by a%, then its area changes by
(
2a +
a2 / 100
)
%
Here, a = 1
Required percentage =
(
2 x 1 +
12 / 100
)
%
= 2 +
1 / 100
=
200 + 1 / 100
=
201 / 100

1 Hectare = 10000 sq m
∴ increase in area =
201 x 10000 / 100 x 100
= 201
Hence, the difference in areas is 201 sq m.

124. If diameter of a circle is increased by 12%, find the percentage increased in its circumference.
  A.  12%
  B.  9%
  C.  15%
  D.  11%
     
   
View Answer

Shortcut:
If all the measuring sides of any two-dimensional figure is changed (increase or decrease) by a%, then its perimeter also changes by the same percentage, i.e, a%. Here, a = 12
Required percentage = 12%

125. If the sides of a rectangle are increased each by 10%, find he percentage increase in its diagonals.
  A.  13%
  B.  12%
  C.  9%
  D.  10%
     
   
View Answer

Shortcut:
If all sides of a quadrilateral are increased by a%, then its corresponding diagonals also increased by a%.
Here, a = 10
Required percentage = 10%

126. If the length and the two diagonals of a rectangle are each increased by 9%, then find the percnetage inicrease in its breadth.
  A.  7%
  B.  9%
  C.  11%
  D.  8%
     
   
View Answer

Shortcut:
If all sides of a quadrilateral are increased by a%, then its corresponding diagonals also increased by a%.
Here, a = 9
Required percentage = 9%

127. A parallelogram, the length of whose sides are 12 cm and 8 cm, has one diagonal 10 cm long. Find the length of the other diagonal.
  A.  17.2 cm
  B.  18.2 cm
  C.  17.8 cm
  D.  16.6 cm
     
   
View Answer

Shortcut:
If a parallelogram, the length of whose sies are 'a' cm and 'b' cm, has one diagonal 'd' cm long, then the length of the other diagonal is
√[
2
(
a2 + b2 −
d2 / 2
)]
m

Here, a = 12, b = 8, d = 10
Required length =
√[
2
(
122 + 82 −
102 / 2
)]

=
√[
2
(
144 + 64 −
100 / 2
)]

= √[2(144 + 64 − 50)]
= √[2(144 + 64 − 50)]
= √[2(158)] = √(316) = 17.8 (approx)

128. A semi-circle is constructted on each side of a square of length 2 m. Find the area of the whole figure.
  A.  (4 + 2π)
  B.  (4 + 4π)
  C.  (4 + π)
  D.  (4 + 3π)
     
   
View Answer

Shortcut:
If a semi-circle is constructed on each side of a square of length 'a' m, then the area of the whole figure is given by
[
a2 / 2
(2 + π)
]
sq m
Here, a = 2
Required area =
[
22 / 2
(2 + π)
]
= (4 + 2π) sq m

129. The area of a circle is halved when its radius is decreased by n. Find its radius.
  A.  
√5n / √5 − 1
  B.  
√2n / √2 − 1
  C.  
√3n / √3 − 1
  D.  
√2n / √2 − 3
     
   
View Answer

Shortcut:
If the radius of a circle is decreased by 'a' metres, then the ratio of the area of the original circle to the reduced circle becomes c : d. The radius is given by
a / 1 − √(c/d)

Here, a = n, c = 1, d = 2
Required radius =
n / 1 − √(1/2)

=
n / 1 − (1/√2)

=
n / (√2 − 1)/√2)

=
√2n / √2 − 1

130. A cord is in the form of a square enclosing an area of 22 cm2. If the smae cord is bent into a circle, then find the area of that circle.
  A.  22 cm2
  B.  25 cm2
  C.  28 cm2
  D.  20 cm2
     
   
View Answer

Shortcut:
If the area of a square is 'a' sq units, then area of the circle formed by the same perimeter is given by
4a / π
sq units or,
14a / 11
sq units
Here, a = 22
Required area =
4 x 22 / 22/7
= 4 x 7 = 28
Hence, the area of that circle is 28 sq cm.

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