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  • A hollow cube of internal edge 22cm 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 is (A) 142296

A hollow cube of internal edge 22cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that \frac{1}{8} space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is

(A) 142296                  (B) 142396                  (C) 142496                  (D) 142596

Answers (1)

Answer(A) 142296    

Solution

            Diameter of marble = 0.5 cm

            Radius \frac{0.5}{2}=\frac{5}{20}=\frac{1}{4}cm

            Volume of marble \frac{4\pi r^{3}}{3}=\frac{4}{3}\times \frac{22}{7} \times \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} =\frac{11}{168}cm^{3}

                                                   

            Edge of cube = 22 cm

            Volume (V) 22 \times 22 \times 22

            Space occupied by marble = total volume \frac{1}{8}  part of volume

                        =v -\frac{1}{8}v=\frac{7v}{8}

            Number of marble =\frac{space occupied }{volume of marble}

                        =\frac{7v \times 168 }{8 \times 11}

                        =\frac{7 \times 22\times 22\times 22\times 22\times 168 }{8 \times 11}

                        =142296

Posted by

infoexpert21

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