Question

a cube of lead with edges measuring 6 cm is melted and form into 27 equal cubes what will be the length of the edges of the new cubes

Answer 1

Edges of large cube = 6cm
Edge of 1 small cube = x

Volume of large cube = volume of small cubes

Volume of large cube=(edge)^3
Volume of small 27 cube=(edge)^3×27
So,
Volume of large cube=Volume of 27 small cubes
(edge)^3 = (edge)^3×27
(6)^3 = (x)^3×27
216 = (x)^3×27
216 ÷ 27 = (x)^3
8 = (x)^3
√8 = x
2 = x
so, edge of cubes = 2

Answer 2

Answer:

The length of the edges of the new cubes is 2cm.

Step-by-step explanation:

Given

A cube of lead with edges measuring 6 cm is melted and formed into 27 equal cubes.

To find

The length of the edges of the new cubes.

Step 1

Let the edge of the small cubes = x cm.

Then, the Volume of the larger cube $=27*Volume of small cubes.$

$\Rightarrow(6)^{3}=27 \times(\mathrm{x})^{3} \Rightarrow \frac{216}{27}=\mathrm{x}^{3}$

$\Rightarrow x^{3}=8 \Rightarrow x=\sqrt[3]{8}=2 \mathrm{~cm}$

Therefore,

The length of the edges of the new cubes is 2cm.

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