Question

In a Maths lab there are some cubes and cuboids of the following measurements:
I) one cube of side 4cm
II) 3 cuboids each of dimensions 4cmX4cmX6cm and 3 cuboids each of dimensions 4cmX6cmX6cm

A student wants to arrange these cubes and cuboids in the form of a big cube. Is it possible for him/her to arrange them in the form of a big cube? If yes, then find the length of each side of the new cube formed.

Answer 1

area of 1st cube 4*4*4cm² i.e. 64cm³
area of 2nd 3 cuboids are96cm³
and the next 3 cuboids are156cm³
therefore total area is 64+96*3+156*3 is equal to 820cm³

no since 820 is not a perfect cube

Answer 2

Answer:

Yes possible

Length of side of new cube = 10 cm

Question is:

In a maths lab there are some cubes and cubiods of the following measurements:

1 one cube of side 4cm

2 one cube of side 6cm

3 three cuboids each of dimensions 4cm ×4 cm ×6 cm and 3 cuboids each of dimensions 4cm×6cm×6cm.

A student wants to arrange these cubes and cuboids in the form of a big cube

Step-by-step explanation:

Yes, it is possible.

We know that

(a + b)³ = a³+ 3a²b + 3ab² + b³

⇒ (4 + 6)³ = 4³ + 3 × 4²× 6 + 3 × 4 × 6²+ 6³

⇒ (10³ = (4)³ + 3*( 4 × 4× 6 )+ 3*( 4 × 6 × 6) + (6)³

∴ Length of side of new cube = 10 cm