1.  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 :

the volume of the box
twice the volume of the box
the square of the volume of the box
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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2.  The volume of a rectangle block of stone is 10368 dm3. Its dimensions are in the ratio of 3 : 2 : 1. If its entire surface is polished at 2 paise per dm2, then the total cost will be :

Rs. 31. 50
Rs 31.68
Rs 63
Rs. 63. 36

```Answer

Answer: Option  D Explanation:Let the dimensions be 3x, 2x and x respectively, Then,
3x * 2x * x = 10368
= x3 = (10368⁄6) = 1728
= x = 12.
So, the dimensions of the block are 36 dm, 24 dm, and 12 dm.
Surface area = [2 (36 * 24 + 24 * 12 + 36 * 12)] dm2
= [2 * 144(6 + 2 + 3)] dm2 = 3168 dm2.
Cost of polishing = Rs. (2 * 3168⁄100) = Rs. 63. 36 ```

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3.  An open box is made of wood 3 cm thick. It external dimensions are 1.46 m, 1.16m and 8.3 dm. The cost of painting the inner surface of the box at 50 paise per 100 sq. cm is :

Rs. 138.50
Rs 277
Rs. 415.50
Rs 554

```Answer

Answer: Option  B Explanation:Internal length = (146 - 6) cm= 140 cm.
Internal breadth (116 - 6) cm = 110 cm.
Internal depth = (83 - 3) cm= 80 cm.
Area of inner surface = [2(l + b) * h]  + lb.
= [2(140 + 110) * 80 + 140 * 110] cm2 = 55400 cm2.
Cost of painting      = Rs. (1⁄2 * 1⁄100 * 55400) = Rs. 277 ```

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4.  Total surface area of a cube whose side is 0.5 cm is :

14 cm2
18 cm2
34 cm2
32 cm2

```Answer

Answer: Option  D Explanation:Surface area = [ 6 * (1⁄2)2] = 3⁄2 cm2. ```

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5.  In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is :

75 cu. m
750 cu. m
7500 cu. m
75000 cu. m

```Answer

Answer: Option  B Explanation:Area   = (1.5 * 10000) m2 = 15000 m2.
Depth  = 5⁄100m = 1⁄20m.
Volume = (Area * Depth) = (15000 * 1⁄20)m3 = 750 m3. ```

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