โ† 6th Grade Math ๐Ÿ† Green Badge
Unit 4 ยท Geometry ยท 6.G

๐Ÿ“ฆ Eco-Friendly Package Designer

A logistics company hires you to design packaging that holds the product while wasting the least cardboard. Fold nets into boxes, measure surface area and volume, and earn the Green Badge.

Deconstruct

The core idea

Surface area is the cardboard you need (flatten the box into its net and add up every face). Volume is the product it holds (stack unit cubes inside). For a fixed volume, a cube-like shape has the least surface area โ€” the lowest waste.

Do ยท Origami Folding Nets

Fold the net into a box

Set the dimensions, press Assemble to fold the 2D net into a 3D prism, and watch the surface area and volume update.

56
surface area
24
volume
2.33
SA รท V ratio
TOP
BASE
FRONT
BACK
L
R
Deliver ยท Boss Level

โ™ป๏ธ The Eco-Audit

Design a package that holds exactly 24 cubic units of product using the least cardboard โ€” get the surface-area-to-volume ratio down to 2.20 or lower to earn the Green Badge. Adjust the dimensions above, then submit your audit.

Current: V = 24, ratio = 2.33 โ€” too wasteful. Reshape to V = 24 with ratio โ‰ค 2.20.
๐Ÿ† Minimal waste! You earned the Green Badge โ€” saved to this device.

Grounded in CA CCSS-M, Grade 6 ยท 6.G (nets, surface area, and volume of right prisms). The fold is a CSS-3D illustration; the SA/V math is exact. Part of the 4-D series.