To find the volume of the remaining wood after cutting a square hole through a cube, we need to follow these steps:
1. Calculate the volume of the original cube:
- The side length of the cube is 5 cm.
- The volume of a cube is given by the formula [tex]\( V = \text{side}^3 \)[/tex].
- So, [tex]\( V_{\text{cube}} = 5 \times 5 \times 5 = 125 \)[/tex] cubic centimeters (cm³).
2. Calculate the volume of the hole:
- The hole is a square prism with a side length of 3 cm and it goes through the entire height of the cube (which is 5 cm).
- The volume of a prism (or hole in this case) is given by the formula [tex]\( V = \text{base area} \times \text{height} \)[/tex].
- The base area of the hole (which is a square) is [tex]\( \text{side}_{\text{hole}} \times \text{side}_{\text{hole}} = 3 \times 3 = 9 \)[/tex] square centimeters (cm²).
- So, the volume of the hole is [tex]\( V_{\text{hole}} = 9 \times 5 = 45 \)[/tex] cubic centimeters (cm³).
3. Calculate the volume of the remaining wood:
- The remaining wood is the original volume of the cube minus the volume of the hole.
- So, [tex]\( V_{\text{remaining}} = V_{\text{cube}} - V_{\text{hole}} = 125 - 45 = 80 \)[/tex] cubic centimeters (cm³).
Thus, the volume of the remaining wood after the hole is cut through the cube is 80 cubic centimeters (cm³).
