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

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
(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}
                         = 11/168 cm^{3}
Edge of cube = 22 cm
Volume (V) =22\times 22 \times 22
Space occupied by marble = total volume - 1/8 th part of the 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 168}{8\times11}
                            =142296

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