# a hollow cube of internal edge 22cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that 1/8th space of the cube remains unfilled. then the number of marbles that the cube can accommodate is

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## 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 is

Click here👆to get an answer to your question ✍️ 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 is

A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed thatQuestion 8 1

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

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Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is A)

Volume of hollow cube =(22)3 Radius of marble = 2 0.5 = 4 1

Volume of each marble =4πr

3 = 3 4 × 7 22 × 4 1 × 4 1 × 4 1 = 168 11 cm 3

Space of cube occupied by marbles =V−

8 1 V = 8 7V

∴ Number of marbles =

168 11 8 7V = 168 11 8 7 ×22×22×22 =142,296

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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

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

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 isa. 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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A mason constructs a wall of dimensions 270cm × 300cm × 350cm with the bricks each of size 22.5cm × . . . .

## Question 8 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 is Thinking process If we divide the total volume filled by marbles in a cube by volume of a marble, then we get the required number of marbles.A 142296B 142396C 142496D 142596

Question 8 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 is Thinking process If we divide the total volume filled by marbles in a cube by volume of a marble, then we get the required number of marbles.A 142296B 142396C 142496D 142596

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Question 8 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 is Thinking process If we divide the total volume filled by marbles in a cube by volume of a marble, then we get the required number of marbles.A 142296B 142396C 142496D 142596

Question

**Question 8**

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 is

Thinking process- If we divide the total volume filled by marbles in a cube by volume of a marble, then we get the required number of marbles.

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

EXEMP - Grade 10 - Mathematics - Surface Areas and Volumes - Q8

MATHEMATICS

06:00 Min | 16 Views

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Option (A) is correct.

Given , edge of the cube = 22 cm

∴ Volume of the cube = 22 3 = 10648 c m 3 [Volume of cube = s i d e 3 ]

Also, given diameter of marble = 0.5 cm

∴ Radius of a marble, ⇒ r = 0.5 2 = 0.25 c m [Diameter = 2 × r a d i u s ]

Volume of one marble

= 4 3 π r 3 = 4 3 × 22 7 × ( 0.25 ) 3 Volume of sphere = 4 3 × π ( r a d i u s ) 3 = 1.375 21 = 0.0655 c m 3

Filled space of cube = Volume of the cube - [

1 8 × Volume of cube ] = 10648 − ( 10648 × 1 8 \ = 10648 × 7 8 = 9317 c m 3 ∴

Required number of marbles

= T o t a l s p a c e f i l l e d b y m a r b l e s i n a c u b e V o l u m e o f o n e m a r b l e = 9317 0.0655 = 142244 ~ (approx.)

**Hence, the number of marbles that cube can accommodate is 142244.**

Suggest Corrections 6

SIMILAR QUESTIONS

**Q.**A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and

18

space of the cube remains unfilled. Number of marbles required is

(a) 142296 (b) 142396 (c) 142496 (d) 142596

**Q.**

**Question 8**

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 is

Thinking process- If we divide the total volume filled by marbles in a cube by volume of a marble, then we get the required number of marbles.

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

**Q.**A hollow cube of internal edge

22 c m

is filled with spherical marbles of diameter

0.5 c m

and it is assumed that

1 8

space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is

**Q.**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 is

**Q.**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 accomodate is

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Guys, does anyone know the answer?