Q22 of 35 Page 74

The weight of the wooden box made of wooden plate with thickness of 5cm along with its covering is115.5kg, but the weight of box filled with rice is 880.5kg.The length and breadth of inner side of the box are 12dcm and 8.5dcm respectively and weight of 1 cubic dcm rice is 1.5kg .Let us calculate the inner height of the box after calculation. Let us calculate the total expenditure to colour the outside of the box, if rate is Rs 1.5 per sq. dcm.

Given, thickness = 5cm = 0.5dm

weight of empty box = 115.5 kg


weight of filled box = 880.5 kg


Length of inner side of box = 12dcm


breadth of inner side of box = 8.5 dcm


According to question, volume of rice inside the box = Inner capacity of box


weight of filled box-weight of empty box = length × breadth height


( 880.5-115.5)kg = 12×8.5×h


dcm3 = 102 h {1 cubic dcm rice is 1.5kg}


h =


h = 5 dcm


As, thickness of the box = 0.5dcm


So, outer length of box (L) = inner length + 2xthickness = 12 + 2×0.5 = 13 dcm


outer breadth of box(B) = inner breadth + 2Xthickness = 8.5 + 2×0.5 = 9.5 dcm


outer height of box(H) = inner height + 2X thickness = 5 + 2×0.5 = 6 dcm


As,Outer surface area = 2(LB + BH + LH)


= 2(13×9.5 + 9.5×6 + 6×13)


= 2(123.5 + 57 + 78)


= 2×285.5


= 517 dcm2


According to question, cost of 1 dcm2 = Rs.1.5


So, cost of 517 dcm2 = Rs.(1.5×517)


= Rs 775.5


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