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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.

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 accomodate is
a. 142296
b. 142396
c. 142496
d. 142596

Solution:

It is given that

The internal edge of a hollow cube = 22 cm

Volume of cube = side³ = 22³ = 10648 cm³

Diameter of special marbles = 0.5 cm

Radius of special marbles = 0.5/2 = 1/4 cm

We know that

Volume of one marble = 4/3 πr³

Substituting the values

Volume of one marble = 4/3 × 22/7 × (1/4)³

= 11/168 cm³

Here

Filled space of the cube = Volume of cube - 1/8 volume of cube

= 10648 - 1/8 × 10648

= 10648 × 7/8

= 9317 cm³

So the required number of marbles = total space filled by the marble in one cube/ volume of one marble

= 9317/ (11/168)

= 142296

Therefore, the number of marbles that the cube can accomodate is 142296.

✦ Try This: A hollow cube of internal edge 24cm is filled with spherical marbles of diameter 0.4 cm and it is assumed that 1/5 space of the cube remains unfilled. Then the number of marbles that the cube can accomodate is

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.1 Problem 8

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 accomodate is a. 142296, b. 142396, c. 142496, d. 142596

Summary:

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 accomodate is 142296

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