Question

box 3
sketch:
image of box 3
shape of the base:
length:
width:
height:
formula:
workspace:
volume =

box 4
sketch:
image of box 4
shape of the base:
length:
width:
height:
formula:
workspace:
volume =

one day, a customer bought a breakable artifact from the museum. it was carefully packed in box 4. to be extra careful, mrs. lopez then packed box 4 inside box 3. what volume of packing peanuts did she need to fill the rest of box 3?

Explanation:

Step1: Define Box 3 dimensions

Length = 24, Width = 24, Height = 24

Step2: Box 3 volume formula

Volume of a cube: $V_{\text{box3}} = l \times w \times h$

Step3: Calculate Box 3 volume

$V_{\text{box3}} = 24 \times 24 \times 24 = 13824$

Step4: Define Box 4 dimensions

Base is a triangle with base=24, height=24; prism height=24

Step5: Box 4 volume formula

Volume of triangular prism: $V_{\text{box4}} = \frac{1}{2} \times b \times h_{\text{base}} \times h_{\text{prism}}$

Step6: Calculate Box 4 volume

$V_{\text{box4}} = \frac{1}{2} \times 24 \times 24 \times 24 = 6912$

Step7: Find packing peanut volume

Subtract Box4 volume from Box3 volume: $V_{\text{peanuts}} = V_{\text{box3}} - V_{\text{box4}}$

Step8: Compute final volume

$V_{\text{peanuts}} = 13824 - 6912 = 6912$

Answer:

6912