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1. Find the volume of cuboid 25 m long, 20 m broad and 16 m high.
  A.  7500 cubic metres
  B.  8000 cubic metres
  C.  6000 cubic metres
  D.  8200 cubic metres
     
   
View Answer

Shortcut:
To find volume of a cuboid if its length, breadth and height are given.
Volume of a cuboid = length x breadth x height
Here, length = 25, breadth = 20, height = 16
Using, these values in the shortcut, we get:
Volume of Cuboid = 25 × 20 × 16 = 8000
Hence, the volume of cuboid is 8000 cubic metres.

2. A wooden box of dimensions 8 m × 7 m × 6 m is to carry rectangular boxes of dimesions 8 cm × 7cm × 6 cm. What is the maximum numbers of boxes that can be carried in the wooden box?
  A.  1000000
  B.  100000
  C.  1200000
  D.  900000
     
   
View Answer

Total boxes =
800 × 700 × 600 / 8 × 7 × 6

=1000000

3. The area of a ground is 6500 m2. Find the cost of covering it with cement 1 cm deep, if the cement cost is Rs 3 per cubic metre.
  A.  Rs 185
  B.  Rs 150
  C.  Rs 200
  D.  Rs 195
     
   
View Answer

Volume of cementing = 6500 ×
1 / 100
cu metres = 65 cu m
Cost of cementing = Rs (65 ×3) = Rs 195

4. A container 7 metres high is half as long again as it is broad and its volume is 420 cubic metres. Find its length and breadth.
  A.  breadth = √10 m; length = 3√10 m
  B.  breadth = 2√10 m; length = √10 m
  C.  breadth = 2√10 m; length = 3√10 m
  D.  breadth = 2 m; length = 3 m
     
   
View Answer

Let its breadth = z, then length =
z / 2
+ z =
3z / 2
metres
=
3z / 2
× z × 7 = 420
z2 =
420 × 2 / 3 × 7

z = √40
z = √ 2 × 2 × 2 × 5
z = 2 √ 2 × 5
z = 2 √10 , then length =
3 ×2 √10 / 2

Hence, breadth = 2√10 m and length = 3√10 m

5. How many globes each 0.3 cm in diameter can be made from a cuboid of dimension 12 cm 44 cm 27 cm?
  A.  1108000
  B.  1008000
  C.  1028000
  D.  1198000
     
   
View Answer

Number of sphere =
Volume of cuboid / Volume of 1 sphere

=
12 × 44 × 27 / 1/6 × 22/7 ×0.3 × 0.3 × 0.3

=
12 × 2 × 27 × 7 × 6 × 10 × 10 × 10 / 3 × 3 × 3

= 1008000

6. A field is dugged up 4 m long, 3 m wide and 2.5 m deep. The length of the field is 15 m and its width is 10 m. If the earth dug out is evenly spread out over the field, the level of the field will rise by approximately:
  A.  21.73 cm
  B.  2.17 cm
  C.  19.73 cm
  D.  25 cm
     
   
View Answer

Volume of earth dugged out= 4 × 3 × 2.5 = 30 m3
Area where earth is spread = [(15 × 10) - (4 × 3)] m2] = 138 m2
Therefore, level increased =
30 / 138
m =
30 × 100 / 138
= 21.73 cm

7. A rectangular tank having length 7
1 / 3
m, 15 m in breadth and 2 metres in depth, is full of water. Find the weight of water in metric tons, given that one cubic metre of water weighs 1000 kg.
  A.  240 metric tons
  B.  120 metric tons
  C.  200 metric tons
  D.  220 metric tons
     
   
View Answer

Volume of water = 7
1 / 3
× 15 × 2 m3 = 220 m3
Weight of water = 220 × 1000 kg = 220000 kg = 220 metric tons

8. If the sand of volume 150 m3 is thrown into a water tank 15 m long and 3 m wide, find the level of water that will rise.
  A.  2.3 m
  B.  3 m
  C.  3.3 m
  D.  3.5 m
     
   
View Answer

Let the initial height be h and the new height is H metres. we have to find the difference between new height and height
15 × 3 × (H - h) = 150
H - h =
150 / 15 × 3
=
10 / 3
= 3.3 m

9. A lake 6 m deep and 100 m wide is flowing at the rate of 5
5 / 2
km/hr. Find how many cubic metre of water run into the sea per second.
  A.  950 cubic meter
  B.  1250 cubic meter
  C.  1050 cubic meter
  D.  1550 cubic meter
     
   
View Answer

River speed = 5
5 / 2
km/hr =
15 / 2
km/hr =
15 / 2
×
5 / 18
m/sec =
25 / 12
m/sec
water will run into sea = 6 × 100 ×
25 / 12
=
25 / 12
= 1250 cubic meter

10. A room is to be built to accommodate 56 persons, so as to allow 2.5 sq metres of floor and 11 cubic metres of space for each person. If the room be 7 metres long, what must be its breadth and height>
  A.  8 metres
  B.  5 metres
  C.  18 metres
  D.  15 metres
     
   
View Answer

7 × b = 56 × 2.5
b =
56 × 2.5 / 7
= 20 metres
l × b × h = 56 × 20
h =
56 × 20 / l × b

h =
56 × 20 / 56 × 2.5
= 8 metres

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