Question

What is the largest number of cubes that can be cut from the given cuboidal block if each of the cube has 3 cm sides? 9 cm 7 cm 24 cm​

Answer 1

Answer:

18

Step-by-step explanation:

We have the cuboid of dimensions 10cm×9cm×6cm

We are to find how many cubes with edge 3 cm can be cut from the given cuboid.

Let us cut this cuboid into following two cuboids

9cm×9cm×6cm

And

1cm×9cm×6cm

So, the number of cubes of sides 3 cm, that can be cut from the first cuboid,

⇒  

3cm×3cm×3cm

9cm×9cm×6cm

​

=18

We can not cut a single cube of side 3 cm from the second cuboid of dimensions 1cm×9cm×6cm

Hence, this much volume is unless for us.

So, we can cut maximum 18 cubes of sides 3cm from the cuboid of dimension 10cm×9cm×6cm.

Answer 2

According to the question;

Dimensions of cuboid = 9 cm, 7 cm, 24 cm

Dimension of cubes = 3 cm

now,

Volume of cuboid = length × breath × height

= 9 cm × 7 cm × 24cm

= 1,512 cm³

Volume of cube = (side)³

= (3 cm)³

= 27 cm³

Let the number of cubes can be found  = n, the volume of cuboid = C₁ and the volume of cube = C₂

Now;

$n =\frac{C_{1} }{C_{2} } \\n = \frac{1512 cm^{3} }{3 cm^{3} } \\n = 56$

The number of cubes that can be cut from the given cuboidal block (9 cm, 7 cm and 24 cm​) if each side of the cubes is 3 cm are 56.

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