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11. Area of the base of a cubiod is 9 sq meters, area of side face and area of other side face are 16 sq meters and 25 sq metres respectively.Find the volume of the cubiod.
  A.   65 cu. metres
  B.  60 cu. metres
  C.  40 cu. metres
  D.  50 cu. metres
     
   
View Answer

Shortcut:
To find the volume of a cuboid if its area of base or top, area of side face and area of other side face are given.
Volume of a cuboid = √(A1 x A2 x A3)
where, A1 = Area of base or top
A2 = Area of one side face and
A3 = Area of other side face
Here, A1 = 9, A2 = 16, A3 = 25
Using, these values in the shortcut, we get:
Volume of Cuboid = √(9 x 16 x 25) = √(3600) = 60 cu metres

12. Find the volume of a cubiod whose area of base and two adjacent faces are 180 sq cm, 96 sq cm and 120 sq cm respectively.
  A.  1440 cu cm
  B.  1480 cu cm
  C.  1520 cu cm
  D.  1500 cu cm
     
   
View Answer

Shortcut:
To find the volume of a cuboid if its area of base or top, area of side face and area of other side face are given.
Volume of a cuboid = √(A1 x A2 x A3)
where, A1 = Area of base or top
A2 = Area of one side face and
A3 = Area of other side face
Here, A1 = 180, A2 = 96, A3 = 120
Using, these values in the shortcut, we get:
Volume of Cuboid = √(180 x 96 x 120) = √(2073600) = 1440 cu cm

13. A closed wooden box measures externally 45 cm long, 35 cm broad and 30 cm high, if the thickness of the wood is 2
1 / 2
cm, find the cost of painting the box inside at the rate of Rs 2 per square dm.
  A.  Rs 130
  B.  Rs 121
  C.  Rs 115
  D.  Rs 118
     
   
View Answer

Shortcut:
To find the whole surface area of a cuboid if its length(l), breadth(b) and height(h) are given.
Whole surface area of cuboid = 2(lb + bh + lh)
Here, Internal length (l) = 45 −
5 / 2
x 2 = 40 cm
Internal breadth (b) = 35 −
5 / 2
x 2 = 30 cm
Internal height (h) = 30 −
5 / 2
x 2 = 25 cm
Using, these values in the shortcut, we get:
Whole surface area of cuboid = 2(40 x 30 + 30 x 25 + 40 x 25)
= 2(1200 + 750 + 1000) = 5900 sq cm
∴ Required cost of painting =
5900 x 2 / 10 x 10
= Rs 118

14. The length of the longest rod that can be placed in a room 30 cm long, 24 m broad and 18 m high, is :
  A.  30√4 m
  B.  30√5 m
  C.  30√2 m
  D.  30√3 m
     
   
View Answer

Shortcut:
To find the diagonal of a cuboid if its length (l), breadth (b) and height (h) are given.
Diagonal of cuboid = √(l2 + b2 + h2)
Here, Length of the longest rod = length of diagonal
l = 30, b = 24, h = 18
Using, these values in the shortcut, we get:
Diagonal of cuboid = √(302 + 242 + 182)
= √(900 + 576 + 324) = √(1800) = 30√2
Hence, the length of diagonal is 30√2 m.

15. The sum of length, breadth and height of a cubiod is 25 cm and its diagonal is 15 cm long. Find the total surface area of the cubiod.
  A.  350 sq. cm
  B.  400 sq. cm
  C.  420 sq. cm
  D.  380 sq. cm
     
   
View Answer

Shortcut:
To find total surface area of a cuboid if the sum of all three sides and diagonal are given.
Total surface area = (sum of all three sides)2 − (Diagonal)2
Here, sum of all three sides = 25, diagonal = 15
Using, these values in the shortcut, we get:
Total surface area = (25)2 − (15)2 = 625 − 225 = 400
Hence, the total surface area of the cuboid is 400 sq cm.

16. Find the volume, surface area and the diagonal of a cube, each of whose sides measures 2 cm.
  A.  Volume: 6 cu cm; Surface area: 20 sq. cm; Diagonal: 3√2
  B.  Volume: 5 cu cm; Surface area: 26 sq. cm; Diagonal: 2√3
  C.  Volume: 8 cu cm; Surface area: 24 sq. cm; Diagonal: 2√3
  D.  Volume: 10 cu cm; Surface area: 25 sq. cm; Diagonal: 2√5
     
   
View Answer

Shortcut:
If each edge (or side) of a cube is 'a' units then
(i) Volume of the cube = a3 cubic units
(ii) whole surface of the cube = 6a2 sq units
(iii) diagonal of the cube = √3a units
Note: If diagonal of a cube is given, then the volume of the cube is given by
(
diagonal / √3
)
3
Here, a = 2
Using, this value in the shortcut, we get:
(i) Volume of the cube = (2)3 = 8 cubic cm
(ii) whole surface of the cube = 6 x (2)2 = 6 x 4 = 24 sq cm
(iii) diagonal of the cube = 2√3 units

17. A cubic metre of copper weighting 9000 kilograms is rolled into a square bar 9 metres long. An exact cube is cut off from the bar. How much does it weight?
  A.  327
2 / 5
kg
  B.  333
1 / 7
kg
  C.  330
1 / 5
kg
  D.  333
1 / 3
kg
     
   
View Answer

Shortcut:
If each edge (or side) of a cube is 'a' units then
(i) Volume of the cube = a3 cubic units
(ii) whole surface of the cube = 6a2 sq units
(iii) diagonal of the cube = √3a units
Note: If diagonal of a cube is given, then the volume of the cube is given by
(
diagonal / √3
)
3
Here,
(Area of the square end) x 9 = vol = 1 cubic metres.
∴ side of the square end =
√(
1 / 9
)
=
1 / 3
metre
∴ Vol of the cube =
1 / 3
x
1 / 3
x
1 / 3
=
1 / 27
cubic metre
∴ Weight of cube =
9000 / 27
= 333
1 / 3
kg

18. A cube of metal each edge of which measures 5 cm,weight 0.625 kg. What is the lentgh of each edge of a cube of the same metal which weights 40 kg.
  A.  21cm
  B.  20cm
  C.  15cm
  D.  25cm
     
   
View Answer

Shortcut:
If each edge (or side) of a cube is 'a' units then
(i) Volume of the cube = a3 cubic units
(ii) whole surface of the cube = 6a2 sq units
(iii) diagonal of the cube = √3a units
Note: If diagonal of a cube is given, then the volume of the cube is given by
(
diagonal / √3
)
3
Here, Vol. of cube = 5 x 5 x 5 = 125 cubic cm.
0.625 kg = 125 cubic cm
∴ 40 kg =
125 / 0.625
x 40 = 8000 cubic cm.
∴ edge = √8000 = 20 cm.

19. A hollow garden roller 63 cm wide with a girth of 440 cm is made of iron 4 cm thick.The volume of iron is :
  A.  58752 cu cm
  B.  58852 cu cm
  C.  58648 cu cm
  D.  58760 cu cm
     
   
View Answer

Shortcut:
If the radius of the base of a cylinder is 'r' units and its height (or length) is 'h' units, then volume of the cylinder is given by (πr2h) cubic units.
or Vol. of cylinder = Area of the base of cylinder x Height of cylinder.
Here, h = 63, Circumference = 440
or, 2πr = 440
or, r =
220 / π
=
220 / 22/7
= 10 x 7 = 70
Inner radius = (70 − 4) = 66 cm
Vol. of iron = π[(70)2 − (66)2] x 63
=
22 / 7
x 136 x 4 x 63 = 58752
Hence, the volume of iron is 58752 cubic cm.

20. The circumference of the base of a cylinder is 6 metres and its height is 44 metres. Find the volume.
  A.  121 cu metres
  B.  130 cu metres
  C.  126 cu metres
  D.  125 cu metres
     
   
View Answer

Shortcut:
If the radius of the base of a cylinder is 'r' units and its height (or length) is 'h' units, then volume of the cylinder is given by (πr2h) cubic units.
or Vol. of cylinder = Area of the base of cylinder x Height of the cylinder.
Here, h = 44,
Circumference = 6
2πr = 6
r =
3 / π
=
3 / 22/7
=
3 x 7 / 22

Vol. of cylinder = π(r)2 x h
=
22 / 7
x
21 x 21 / 22 x 22
x 44
= 3 x 21 x 2 = 126
Hence, the volume of cylinder is 126 cubic m.

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