Question

volume of rectangular prisms and rectangular pyramids
part ii
to keep the contents of packages from being damaged, mrs. lopez fills her shipping boxes with environmentally friendly, biodegradable packing peanuts. she needs to know how many packing peanuts she uses each month. she can find that by finding the volume of each shipping box and the quantity sold each month.

box 1
sketch:
image of a rectangular prism labeled box 1 with dimensions 36, 18, 18
shape of the base:
length:
width:
height:
formula:
workspace:
volume =

box 2
sketch:
image of a rectangular pyramid labeled box 2 with dimensions 36, 18, 18
shape of the base:
length:
width:
height:
formula:
workspace:
volume =

Explanation:

Box 1 (Rectangular Prism)

Step1: Identify base shape & dimensions

Shape of the base: Rectangle
Length = $36$, Width = $18$, Height = $18$

Step2: State volume formula

$V = \text{Length} \times \text{Width} \times \text{Height}$

Step3: Calculate volume

$V = 36 \times 18 \times 18 = 36 \times 324 = 11664$

Box 2 (Rectangular Pyramid)

Step1: Identify base shape & dimensions

Shape of the base: Rectangle
Length = $18$, Width = $18$, Height = $36$

Step2: State volume formula

$V = \frac{1}{3} \times \text{Length} \times \text{Width} \times \text{Height}$

Step3: Calculate volume

$V = \frac{1}{3} \times 18 \times 18 \times 36 = \frac{1}{3} \times 11664 = 3888$

Answer:

Box 1

Shape of the base: Rectangle
Length: $36$, Width: $18$, Height: $18$
Formula: $V = lwh$
Workspace: $36 \times 18 \times 18 = 11664$
Volume = $11664$

Box 2

Shape of the base: Rectangle
Length: $18$, Width: $18$, Height: $36$
Formula: $V = \frac{1}{3}lwh$
Workspace: $\frac{1}{3} \times 18 \times 18 \times 36 = 3888$
Volume = $3888$