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If a hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that `(1)/(8)` space of the cube remains unfilled. Then, the number of marbles that the cube can accommodate isA. 142244B. 142344C. 142444D. 142544 |
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Answer» Correct Answer - A Given , edge of the cube = 22 cm `therefore` Volume of the cube `= (22)^(3) = 10648 cm^(3) " "[because "Volume of cube " = ("Side")^(3)]` Also, given diameter of marble = 0.5 cm `therefore` Radius of a marble, `r = (0.5)/(2) = 0.25 cm" " [because diameter = 2 xx radius]` volume of one marble `= (4)/(3) pi r^(3) = (4)/(3) xx (22)/(7) xx (0.25)^(3)" "[therefore " Volume of sphere " (4)/(3) xx pi xx ("radius")^(3)]` `= (1.375)/(21) = 0.0655 cm^(3)` Filled space of cube = Volume of the cube `(1)/(8) xx ` volume of cube `= 10648-10648 xx (1)/(8)` `= 10648 xx (7)/(8) = 9317 cm^(3)` |
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