A block of copper in the shape of a rectangular prism is 12 centimetres long,

Question

6 centimetres wide, and 3 centimetres high. It is melted and recast into a cube.
Determine the edge length of the cube. The square root of 216 is 14.69693846

Answer 1

cm.

To solve this problem, we need to find the volume of the copper block and the volume of the cube, and then use the fact that the volumes are equal to find the edge length of the cube.

The volume of the copper block is:

V1 = length x width x height
V1 = 12 cm x 6 cm x 3 cm
V1 = 216 cubic cm

The volume of the cube is:

V2 = (edge length)^3

We can set V1 equal to V2:

V1 = V2

And substitute the expressions we have for these volumes:

216 = (edge length)^3

To solve for the edge length, we take the cube root of both sides:

(edge length) = cube root of 216
(edge length) = 6 x cube root of 6
(edge length) = 6 x 2.449
(edge length) = 14.696 (rounded to 3 decimal places)

So the edge length of the cube is approximately 14.696 cm.