Question

A metal cube of edge 12 cm is melted and formed inroads three smaller cube. if the edge of two smaller cubes are 6 cm and 8 cm. the edge of the third smaller cube is

Answer 1

here edge of 3rd small cube be X , so 12cube=8cube+6cube+xcube or, 1728=512+216+xcube or,xcube =1000 therefore X=10

Answer 2

Hello!

• Edge of cube, S₁ = 8 m
• Edge of cube, S₂ = 6m
• Edge of a bigger cube = 12 m

$\boxed{\sf Volume \:of\: a \:cube = side^{3}}$

Volume of a bigger cube(V) = (side)³ = (12)³= 1728 m³

ATQ,

♦ Volume of cube, V₁ = 8³ = 512 m³

♦ Volume of cube, V₂ = 6³ = 216 m³

Then,

V = V₁ + V₂ + V₃

1728 = 512 + 216 + V₃

1728 = 728 + V₃

1728 - 728 = V₃

V₃ = 1000

♦ Volume of third cube = 1000 m³

Side³ = 1000

Side = ³√1000

Side = ³√10 × 10 × 10

$\boxed{\sf Side = \sf 10 \:m}$

Hence, The edge of third smaller cube is 10 m.

Cheers!