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Problems on Mensuration, Areas and Volumes - Quantitative Aptitude Problems and Solutions


  • 1. The length of a rectangular plot is 5 1/3, times that of its breadth. If the area of the plot is 270 square metres, then what is its length? 
A.) 120 m
B.) 130 m
C.) 125 m
D.) None of these

Answer: Option 'A'

Let the breadth be x metres. Then, length = 16x/3 metres
x × 16x/3 = 270 
x2 = 8100/16 
x = 90/4 
Length = (16/3) × (90/4) = 120 m

  • 2. The ratio of the length and breadth of a plot is 4 : 3. If the breadth is 40 m less than the length, What is the perimeter of the plot? 
A.) 360 m
B.) 460 m
C.) 560 m2
D.) 650 m

Answer: Option 'C'

Let the length be 4x metres. Then, breadth = 3x metres.
Then, 4x - 3x = 40 => x = 40 
length l = (4 × 40) = 160 m 
breadth b = (3 × 40) = 120 m 
Perimeter = 2(160 + 120) = 2(280) = 560 m

  • 3. A rectangle carpet has an area of 120 square metres and a perimeter of 46 m. The length of its diagonal is: 
A.) 11 m
B.) 12 m
C.) 13 m
D.) 17 m

Answer: Option 'D'

l × b = 120 and 2 (l + b) = 46 => (l + b) = 23 
(l - b)2 = (l + b)2 - 4lb = (23)2 - 4 × 120 = (529 - 480) = 49 => l - b = 7
On solving l + b = 23, l - b = 7, we get : l = 15, b = 8 
Diagonal = √(15)2 + 82 = √(225 + 64) = √289 = 17 m

  • 4. The length of a rectangular plot is 3 1/8, times that of its breadth. If the area of the plot is 320 square metres, then what is its length? 
A.) 110 m
B.) 120 m
C.) 100 m
D.) 130 m

Answer: Option 'C'

Let the breadth be x metres. Then, length = 25x/8 metres
x × 25x/8 = 320 
x2 = 2560/25 
x = 160/5 = 32 
Length = (25/8) × (32) = 100 m

  • 5. The whole surface area of a cuboid 28 cm long, 16 cm broad and 7.5 cm height, is: 
A.) 1656 cm2
B.) 1546 cm2
C.) 1566 cm2
D.) 1556 cm2

Answer: Option 'D'

Area of the whole surface = 2(lb + bh + lh) 
= 2(28 × 16 + 16 × (15/2) + 28 × (15/2))
= 2(28 × 16 + 8 × 15 + 14 × 15)
= 2(448 + 120 + 210)
= 2(778) = 1556 cm2

  • 6. The length, breadth and height of a cuboid are in the ratio 7 : 5 : 3 and its whole surface area is 27832 cm2. Its volume is: 
A.) 28810 cm2
B.) 28812 cm3
C.) 288120 cm3
D.) 288120 cm2

Answer: Option 'C'

Let, length = 7x cm, breadth = 5x cm and height = 3x cm
Whole surface area = 2(lb + bh + lh) = 2(7x × 5x + 5x × 3x + 7x × 3x) cm2 = (142 x2) cm2
142 x2 = 27832 => x2 = 196 => x = √196 = 14 cm
l = 14 × 7 = 98 cm
b = 14 × 5 = 70 cm
h = 14 × 3 = 42 cm
Volume (l × b × h) = (98 × 70 × 42) cm3 = 288120 cm3

  • 7. The length of the diagonal of a cuboid 32 cm long, 26 cm croad and 20 cm high, is : 
A.) √2100 cm
B.) √2700 cm
C.) √2400 cm
D.) √2800 cm

Answer: Option 'A'

Length of diagonal = √(l2 + b2 + h2)
=> √(322 + 262 + 202)
=> √(1024 + 676 + 400)
=> √2100 cm

  • 8. The length of the diagonal of a cuboid 30 cm long, 24 cm croad and 18 cm high, is : 
A.) 30 cm
B.) 15 cm
C.) 30√2 cm
D.) 13√2 cm

Answer: Option 'C'

Length of diagonal = √(l2 + b2 + h2)
=> √(302 + 242 + 182)
=> √(900 + 576 + 324)
=> √1800 cm
=> √(900 × 2) = 30√2 cm

  • 9. A room is 12 1/4 m long and 7 m wide. The maximum length of a square tile to fill the floor of the room with whole number of tiles should be: 
A.) 175 cm
B.) 150 cm
C.) 200 cm
D.) 125 cm

Answer: Option 'A'

l = 378 cm and b = 700 cm
Maximum length of square tile = H.C.F of (1225 cm, 700 cm) = 175 cm.

  • 10. The perimeter of a floor of a room is 17 m. What is the area of four walls of the room, if its height is 4 m? 
A.) 76 sq. m
B.) 48 sq. m
C.) 54 sq. m
D.) 68 sq. m

Answer: Option 'D'

Perimeter = 2(l + b) × h = 17 m and height = 4m
Area of 4 walls = 2(l + b) × h = (17 × 4) sq. m = 68 sq. m

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