Let's solve this problem step-by-step:
1. Calculate the volume of the cube without the hole:
- The side length of the cube is given as [tex]\(5 \, \text{cm}\)[/tex].
- The formula for the volume of a cube is [tex]\( \text{side length}^3 \)[/tex].
- Therefore, the volume of the cube is [tex]\( 5 \, \text{cm} \times 5 \, \text{cm} \times 5 \, \text{cm} = 125 \, \text{cm}^3 \)[/tex].
2. Calculate the volume of the hole:
- The side length of the square hole is given as [tex]\(3 \, \text{cm}\)[/tex].
- The hole goes all the way through the cube, so it has the same depth as the cube.
- The formula for the volume of a prism (which the hole effectively is) is [tex]\( \text{Base Area} \times \text{Height} \)[/tex].
- The base of the hole is a square with side length [tex]\(3 \, \text{cm}\)[/tex], so its area is [tex]\( 3 \, \text{cm} \times 3 \, \text{cm} = 9 \, \text{cm}^2 \)[/tex].
- The height (depth) of the hole is the same as the side length of the cube, which is [tex]\( 5 \, \text{cm} \)[/tex].
- Therefore, the volume of the hole is [tex]\( 9 \, \text{cm}^2 \times 5 \, \text{cm} = 45 \, \text{cm}^3 \)[/tex].
3. Calculate the volume of the remaining wood (cube with the hole cut out):
- To find the remaining volume, subtract the volume of the hole from the volume of the original cube.
- The remaining volume is [tex]\( 125 \, \text{cm}^3 - 45 \, \text{cm}^3 = 80 \, \text{cm}^3 \)[/tex].
Therefore, the volume of the remaining wood is [tex]\(80 \, \text{cm}^3\)[/tex].
