A block of copper in the shape of a rectangular prism is 12 centimetres long,
6 centimetres wide, and 3 centimetres high. It is melted and recast into a cube.
Determine the edge length of the cube.
The volume of the original rectangular prism is:
V1 = length x width x height
V1 = 12 cm x 6 cm x 3 cm
V1 = 216 cm^3
Since copper is a homogeneous substance, the volume of the cube obtained when it is melted and recast is equal to V1. Therefore:
V2 = V1
V2 = edge^3
Substituting V1:
edge^3 = 216 cm^3
Taking the cube root:
edge = 6 cm
Therefore, the edge length of the cube obtained after melting and recasting the copper is 6 centimetres.
To determine the edge length of the cube, we first need to find the volume of the rectangular prism and then use that value to find the side length of the cube.
The volume of a rectangular prism is given by the formula: V = l * w * h, where l is the length, w is the width, and h is the height.
Given:
Length (l) = 12 cm
Width (w) = 6 cm
Height (h) = 3 cm
Using the formula, we can calculate the volume of the rectangular prism:
V = 12 cm * 6 cm * 3 cm
V = 216 cm³
Since the block of copper is melted and recast into a cube, the volume should remain the same. So, the volume of the cube is also 216 cm³.
The volume of a cube is given by the formula: V = s^3, where s is the side length of the cube.
Therefore, we can solve for s:
216 cm³ = s^3
Taking the cube root of both sides:
s = ∛216 cm
s ≈ 6 cm
Hence, the edge length of the cube is approximately 6 centimetres.