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Question

Three cuboids of dimensions 5cm×6cm×7cm,4cm×7cm×8cm and×2cm×3cm×13cm are melted and a cube is made. Find the edge of the cube.

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Solution

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=210cm3
Volume of cuboid 2=lbh=224cm3
Volume of cuboid 3=lbh=78cm3

From equation (4) we get
a3=210+224+78
a3=512
a3=(8)3
[a=8]

Hence edge of cube is 8cm.

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