Plastic Recycling Audit

Volume Density & Capacity Analysis

Auditor Name:
Date:

The Objective: This bin is designed exclusively for 600ml plastic bottles. To calculate the "Overflow Point" (Max Capacity), we must first determine the precise internal volume of the compound shape.

1. Geometric Measurement

Part 1: The Cuboid Base

Length (L):

Width (W):

Base Height (h):

Part 2: The Triangular Peak

Peak Vertical Height:

Prism Length:

2. Mathematical Derivation

Total Capacity Calculation:

Calculate \( V_{\text{Total}} = V_{\text{Base}} + V_{\text{Peak}} \). Show all substitution steps.

Total Volume (cm³) =

3. The "Bottle Density" Challenge

The Packing Problem:

A standard 600ml bottle effectively occupies 750 cm³ of space (due to its cylindrical shape creating air gaps between bottles).

A. How many bottles can mathematically fit?
B. Why is the real-world number usually lower than the mathematical number?

4. Sustainability & Optimization

Crushed vs. Uncrushed:

If students crush the bottles, the effective volume reduces to 200 cm³ per bottle. Calculate the new capacity and explain how this impacts the school's waste collection schedule.