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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)

best_answer

 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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