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

1.

A typist uses a paper 30 cm × 15 cm. He leaves a margin of 2.5 cm at the top and the bottom and 1.25 cm on either side. What percentage of paper area is approximately available for typing? 

   A.) 65%
   B.) 70%
   C.) 80%
   D.) 60%

Answer: Option 'D'

Total area = (30 × 15) cm2 = 450 cm2
Area used = [(30 - 1.25 × 2) × (15 - 2.5 × 2)]
=(27.5 × 10) cm2 = 275 cm2
Percentage of area used = [(275/450) × 100]% = 61.1%~60%(approx..)

2.

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

3.

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

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 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

7.

The diagonal of a square is 30 m. The area of the square is:

   A.) 40 m2
   B.) 450 m2
   C.) 250 m2
   D.) 200 m2

Answer: Option 'B'

Area = 1/2 × (diagonal)2
Area = 1/2 × 30 × 30 m2 = 450 m2

8.

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

9.

The area of the largest triangle that can be inscribed in a semicircle of radius r cm, is: 

   A.) 2r2 cm2
   B.) r2 cm2
   C.) (1/2)r2 cm2
   D.) 2r2 cm2

Answer: Option 'B'

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

10.

The total cost of flooring a room at Rs 8.50 per square metre is Rs 510. If the length of the room is 8 m, its breadth is: 

   A.) 12.5 m
   B.) 10.5 m
   C.) 8.5 m
   D.) 7.5 m

Answer: Option 'D'

Area = (Total cost/Rate) = 510/8.50) m2
= (510 ×(2/17)) m2 = 60 m2
Area = 60 m2
length = 8 m
Breadth = Area/Length = 60/8 = 7.5 m

11.

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.

12.

If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, the area of the rectangle is. 

   A.) 150 cm2
   B.) 120 cm2
   C.) 110 cm2
   D.) 100 cm2

Answer: Option 'B'

2(l + b) = 46 => (l + b) = 23
√(l2 + b2) = 17
=> (l2 + b2) = 289
(l2 + b2) = (l + b)2 - 2lb
=> 289 = (232 - 2lb
=> 2lb = (23)2 - 289 =(529 -289) = 240
=> lb = 120
Area = 120 cm2

13.

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

14.

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

15.

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

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