Question

Bradley cut a square hole out of a block of wood in wood shop. If the block was cube-shaped with side lengths of 9 inches, and the hole had side lengths of 3 inches, how much wood was left after the hole was cut out?

Answer 1

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