To solve this problem, let's break it down step-by-step:
1. Find the length of one edge of the original cube:
- Given the area of one face of a cube is 36 square feet.
- Each face of a cube is a square, and the area of a square is given by [tex]\((\text{edge length})^2\)[/tex].
- So, if [tex]\(A\)[/tex] is the area of the face and [tex]\(a\)[/tex] is the edge length, we have [tex]\(a^2 = 36\)[/tex].
- Solving for [tex]\(a\)[/tex], we get [tex]\(a = \sqrt{36} = 6\)[/tex] feet.
2. Determine the length of the edge of the new cube:
- The edges of the new cube are twice as long as those of the original cube.
- Therefore, if the original edge length is 6 feet, the new edge length is [tex]\(2 \times 6 = 12\)[/tex] feet.
3. Calculate the volume of the new cube:
- The volume of a cube is given by [tex]\((\text{edge length})^3\)[/tex].
- Using the new edge length of 12 feet, the volume is [tex]\(12^3 = 12 \times 12 \times 12\)[/tex].
- Performing the calculation gives [tex]\(12 \times 12 = 144\)[/tex] and then [tex]\(144 \times 12 = 1728\)[/tex] cubic feet.
Therefore, the volume of the new cube with edges that are twice as long is 1,728 cubic feet. The correct answer is 1,728 ft³.
