Question

In a maths lab there are some cubes and cuboid of the following measurements 1 cube of side 4 centimetre 1 cube of side 6 CM three cuboid each of the dimension 4cm 4 centimetre into 6 CM each of dimension 4 cm into 6 into 6cm a student wants to arrange this cubes and cuboid in the form of big cube is it possible for him her to arrange then in the form of big cube if yes then find the length of side of new cubes of form

Answer 1

Step-by-step explanation:

Three cuboid of dimension 5cm×6cm×7cm

4cm×7cm×8cm & 2cm×3cm×13cm

are melted & converted into cube.

Cuboid 1=5cm×6cm×7cm …………(1)

Cuboid 2=4cm×7cm×8cm ………….(2)

Cuboid 3=2cm×3cm×13cm ……………(3)

Now volume of cuboid (1+2+3)= volume of cube (2)

Let 'a' be the edge of cube formed then

Volume of cuboid 1=lbh=210cm

3

Volume of cuboid 2=lbh=224cm

3

Volume of cuboid 3=lbh=78cm

3

From equation (4) we get

a

3

=210+224+78

a

3

=512

a

3

=(8)

3

[a=8]

Hence edge of cube is 8cm.