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 square root of 216 is 14.69693846
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.
To determine the edge length of the cube, we need to find the volume of the rectangular prism and then equate it to the volume of the cube.
The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, the volume of the prism is:
Volume of prism = length x width x height
Volume of prism = 12 cm x 6 cm x 3 cm
Volume of prism = 216 cm³
Since the block is melted and recast into a cube, the volume of the cube must be equal to the volume of the prism. Therefore, the volume of the cube is also 216 cm³.
The volume of a cube is calculated by taking the edge length cubed. Let's represent the edge length of the cube as "x". Therefore, the volume of the cube is:
Volume of cube = x³
Equating the volume of the cube to the volume of the prism, we have:
x³ = 216 cm³
To find the edge length of the cube, we need to find the cube root of 216. Taking the cube root of a number is the reverse operation of cubing a number.
The cube root of 216 is approximately 6. Therefore, the edge length of the cube is 6 centimetres.