how many solid cubes of 3 cm edge can be cut out of a solid cube of 18 cm edge?

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How many solid cubes of 3 cm edge can be cut out of a solid cube of 18 cm edge?A. 232B. 216C. 484D. 36

How many solid cubes of 3 cm edge can be cut out of a solid cube of 18 cm edge?A. 232B. 216C. 484D. 36

Byju's Answer Standard VIII Mathematics Volume of a Cube How many soli... Question

How many solid cubes of 3 cm edge can be cut out of a solid cube of 18 cm edge?

A 36 B 232 C 216 D 484 Open in App Solution

The correct option is B 216

Given, edge length of the larger cube = 18 cm

and, edge length of the smaller cube = 3 cm

The volume is the space occupied by a body .So cutting an object does not change its volume.

So, number of smaller cubes × volume of each smaller cube = volume of the larger cube

Let 'n' be the number of smaller cubes.

Then, n =

volume of larger cube

volume of a smaller cube

We know, volume of a cube of side 'a' is

a 3 . ⇒ n = 18 × 18 × 18 3 × 3 × 3 ∴ n = 216

So, the number of solid cubes of 3 cm that can be cut out of a solid cube of 18 cm is 216.

Volume of a Cube

Standard VIII Mathematics

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[Solved] How many cubes of 3 cm edge can be cut out from a cube of 18

Given: The edge length of cube = 3 cm Formula used: Volume of cube = (side)3 Calculation: Let the number of cubes that can be cut from bigger cube be N An

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How many cubes of 3 cm edge can be cut out from a cube of 18 cm edge?

216 27 125 64

Answer (Detailed Solution Below)

Option 1 : 216

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Detailed Solution

Download Solution PDF

Given:

The edge length of cube = 3 cm

Formula used:

Volume of cube = (side)3

Calculation:

Let the number of cubes that can be cut from bigger cube be N

And we know that,

N × Volume of smaller cube = Volume of bigger cube

⇒ N × (3)3 = (18)3 ⇒ N = (18)3/(3)3 ⇒ N = 216

∴ Number of cubes that can be cut from bigger cube is 216.

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How many cubes of 3 cm edge can be cut out of a cube of 18 cm edge?

Click here👆to get an answer to your question ✍️ How many cubes of 3 cm edge can be cut out of a cube of 18 cm edge?

Question

How many cubes of 3 cm edge can be cut out of a cube of 18 cm edge?

A

36

B

216

C

218

D

432

Hard Open in App Solution Verified by Toppr

Correct option is B)

Given,

Edge of large cube =18cm.

Edge of small cube $$=3cm$.

We know, volume of a cube V=a

3

, where a is the edge of the cube.

Then,

Volume of large cube =(18)

3 =5832cm 3 .

Volume of small cube =(3)

3 =27cm 3 .

Now, Number of cubes =

Volume of small cube

Volume of large cube

​ = 27 5832 ​ =216.

Hence, 216 cubes can be cut out from the cube of 18cm edge.

Thus, option B is correct.

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