To solve this problem, you must follow the proccedure below:
1. The block was cube-shaped with side lengths of 9 inches and to calculate its volume (V1), you must apply the following formula:
V1=s³
s is the side of the cube (s=9)
2. Therefore, you have:
V1=s³
V1=(9 inches)³
V1=729 inches³
3. The lengths of the sides of the hole is 3 inches. Therefore, you must calculate its volume (V2) by applying the formula for calculate the volume of a rectangular prism:
V2=LxWxH
L is the length (L=3 inches).
W is the width (W=3 inches).
H is the heigth (H=9 inches).
4. Therefore, you have:
V2=(3 inches)(3 inches)(9 inches)
V2=81 inches
5. The amount of wood that was left after the hole was cut out, is:
Vt=V1-V2
Vt=648 inches³