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

 Option

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

 Option

Let the dimensions be 3x, 2x and x respectively, Then, 3x * 2x * x = 10368 = x3 = (103686) = 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 * 3168100) = 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

 Option

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. (12 * 1100 * 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

 Option

Surface area = [ 6 * (12)2] = 32 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

 Option

Area = (1.5 * 10000) m2 = 15000 m2. Depth = 5100m = 120m. Volume = (Area * Depth) = (15000 * 120)m3 = 750 m3.

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