Volume

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21. The areas of the three adjacent faces of a rectangular box which meet in a point are known. The product of these areas is equal to :

A.  the volume of the box
B.  twice the volume of the box
C.  the square of the volume of the box
D.  the cube root of the volume of the box

Answer

 Answer: Option  C
 Explanation:
Let length = l, breadth = b and height = h, Then,
Product of areas of 3 adjacent faces = (lb * bh * lh) = (lbh)² = (Volume)².

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22. The capacity of a tank of dimensions (8 m * 6 m * 2.5 m) is

A.  120 litres
B.  1200 litres`
C.  12000 litres
D.  120000 litres

Answer

 Answer: Option  D
 Explanation:
Capacity of the bank = Volume of the tank
                     = (8*100*6*100*2.5*100 ⁄ 1000) litres = 120000 litres.

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23. The edge of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm². The volume of the cuboid is :

A.  24 cm³
B.  48 cm³
C.  64 cm³
D.  120 cm³

Answer

 Answer: Option  B
 Explanation:
Let the dimensions of the cuboid be x, 2x and 3x
Then, 2( x * 2x + 2x * 3x + x * 3x) = 88.
      2x² + 6x² + 3x² = 11x² = 44 
      = x² = 4 
      = x = 2.
Volume of the cuboid = (2 * 4 * 6) cm³ = 48 cm³

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24. The height of a wall is six times its width and the length of the wall is seven times its height. If volume of the wall be 16128 cu. m, its width is :

A.  4 m
B.  4.5 m
C.  5 m
D.  6 m

Answer

 Answer: Option  A
 Explanation:
Let the width of the wall be x metres.
Then, height = (6x) metres and length = (42x) metres.
             = 42x * x * 6x = 16128 
             = x³ = (¹⁶¹²⁸⁄_{42 * 6}) = 64
             = x = 4.

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25. The maximum length of a pencil that can be kept in a rectangular box of dimensions 8 cm * 6 cm * 2 cm is :

A. 2

\sqrt{13}

cm
B. 2

\sqrt{14}

cm
C. 2

\sqrt{26}

cm
D. 10

\sqrt{2}

Answer

 Answer: Option  C
 Explanation:
Required length =  $\sqrt{82+  62+ 22}$  cm =  $\sqrt{104}$  cm = 2 $\sqrt{26}$  cm.

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