Problems on Areas : Aptitude Test

1.

Of the two square fields, the area of the one is 1 hectare, while anothe one is broader by 1%. There differences in area is:

   A.) 200 m
   B.) 201 m
   C.) 201 m2
   D.) None of these

Answer: Option 'C'

Area of one square field = 10000 m2 
10000 × 1 = 10000 
Side of this field = √10000 m = 100 m 
Side of another square = 101 m 
Difference of areas = [ 1012 - 1002 ] m2 
[101+100][101-100] m2
(201)(1) m2 = 201 m2

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2.

Find the cost of carpenting a room 13 m long and 9 m broad with a carpet 100 Cm broad at the rate of Rs.20 per meter.

   A.) 117 m
   B.) 107 m
   C.) 116 m
   D.) 117 m2

Answer: Option 'A'

Area of the carper = Area of the room 
= 13 × 9 => 117 m2 
Breadth of the carpet = 100 cm = 1m 
Length of carpet = Area/Breadth => 117/1 = 177 m.

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3.

A girl walking at the rate of 9 Km per hour crosses a square field diagonally in 12 seconds. The area of the field is: 

   A.) 460 sq.m
   B.) 600 sq.m
   C.) 510 sq.m
   D.) 450 sq.m

Answer: Option 'D'

Distance covered in (9×1000)/(3600) × 12 = 30 m 
Diagonal of squarre field = 30 m. 
area of square field = 302/2
= 900/2 = 450 Sq.m

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4.

The inner circumference of a circle race track 18 m wide is 880 m. Find the radius of the outer circle.

   A.) 140 cm
   B.) 150 m
   C.) 140 m
   D.) None of these

Answer: Option 'C'

Let inner radius be r metres 
Then 2πr = 640 
2 × 22/7 r = 880 
44/7 r = 880 
r = 880 × 7/44 = 140 m

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5.

The perimeter of a square circumscribed about a ciecle of radius r is: 

   A.) 12 r
   B.) 16 r
   C.) 64 r
   D.) 8 r

Answer: Option 'D'

Each side of the square = 2r 
Perimeter of the square = (4×2r) = 8r

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6.

The area of a square field is 4802 m2 the length of its diagonal is: 

   A.) 94 m
   B.) 96 m
   C.) 98 m
   D.) None of these

Answer: Option 'C'

Let the diagonal be d metres, 
Then 1/2 d2 = 4802 
d2 = 9604 
d = √9604 
d = 98 m

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7.

The diagonal of a rhombus are 65 m and 60 m. Its area is:

   A.) 1950 cm^3
   B.) 1950 cm^2
   C.) 1960 cm^2
   D.) 1960 cm^3

Answer: Option ''

Area of the rhombus = 1/2 d1d2 = ( 1/2 × 65 × 60 ) cm2 
= 65 × 30 = 1950 cm2

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8.

The diagonal of a square is 40 m. The area of the square is:

   A.) 800 m2
   B.) 800 m3
   C.) 750 m2
   D.) None of these

Answer: Option 'A'

Arear = 1/2 × ( diagonal )2 
= ( 1/2 × 40 × 40 )m2 
= 1600/2 = 800 m2

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9.

The area of the largest triangle that can be inscribed in a semicircle pf rasius r Cm, is:

   A.) r3 Cm2
   B.) r2 Cm3
   C.) r2 Cm2
   D.) r3 Cm3

Answer: Option 'C'

Area of the largest triangle = (1/2 × 2r × r) cm2 = r2 cm2

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10.

Find the area of the sector whose are is making an angle of 90° at the center of a circle of radius 3.2 Cm. 

   A.) 46.32 Sq.cm
   B.) 54.32 Sq.cm
   C.) 56.22 Sq.cm
   D.) 56.32 Sq.Cm

Answer: Option 'D'

Area of the sector = 90/360 × πr2 
= 90/360 × 22/7 × 3.2 × 3.2 
= (11 × 10.24)/2 = 112.64/2 = 56.32 Sq.Cm

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11.

If the radius of a circle decreased by 50% its area is decreased by:

   A.) 75%
   B.) 50%
   C.) 85%
   D.) 65%

Answer: Option 'A'

Original area = πr2 
New area = π(r/2)2 = (πr2)/4 
Reduction in area = [(πr2 - (πr2)/4]2 = (3πr2)/4 
Reduction percent = ((3πr2)/4 × 1/(πr2 × 100) % = 75%

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12.

A rectangular room 14 m long, 12 m broad is surrounded by a varandah, 3 m wide. Find the area of the varandah? 

   A.) 190 m2
   B.) 170 m2
   C.) 180 m3
   D.) 180 m2

Answer: Option 'D'

Area of varandah = (l+b+2p)2p 
= (14 + 12 + 6 ) 6 
= 180 m2

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13.

The area of the largest circle that can be drawn inside a square of side 28 Cm in length is:

   A.) 616 Cm3
   B.) 626 Cm2
   C.) 619 Cm2
   D.) 616 Cm2

Answer: Option 'D'

Radius of required circle = 14 Cm 
its area = 22/7 × 14 × 14 
44 × 14 = 616 Cm2

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14.

Area of four walls of a room is 99 m2. The length and breadth of the room are 7.5 m and 3.5m respectively. The height of the room is:

   A.) 4.5 Cm
   B.) 5.5 m
   C.) 4.5 m
   D.) 5.5 Cm

Answer: Option 'C'

2(7.5+3.5)×h = 99 
2(11)h = 99 
22h = 99 
h = 99/22 = 9/2 = 4.5 m

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