Scenario: Packaging & Storage - Calculate volumes for shipping boxes and storage containers!
You're designing shipping boxes for different products. Calculate the volume of each box to determine shipping costs and storage capacity.
Box Specifications:
• Rectangular Box: 8 cm × 6 cm × 4 cm
• Cylindrical Container: radius 5 cm, height 12 cm
• Triangular Prism: base 6 cm, height 8 cm, length 10 cm
Rectangular
Cylindrical
Triangular
Visual representation of the 3D shapes
1. Rectangular Box: V = l × w × h
V = 8 × 6 × 4
V = 192 cm³
2. Cylindrical Container: V = πr²h
V = π × 5² × 12
V = π × 25 × 12
V = 300π ≈ 942 cm³
3. Triangular Prism: V = ½ × b × h × l
V = ½ × 6 × 8 × 10
V = ½ × 480
V = 240 cm³
Answer: Rectangular box = 192 cm³, Cylindrical container = 942 cm³, Triangular prism = 240 cm³
V = l × w × h
Volume = length × width × height
Units: cubic units (cm³, m³, etc.)
Example: Box, room, book
V = πr²h
Volume = π × radius² × height
Units: cubic units (cm³, m³, etc.)
Example: Can, tube, pipe
V = ½ × b × h × l
Volume = ½ × base × height × length
Units: cubic units (cm³, m³, etc.)
Example: Roof, wedge, tent
Volume is the amount of space inside a 3D shape. It tells us how much a container can hold or how much space an object takes up.
Think of it like this: If you fill a box with water, the volume is how much water it can hold!
A storage container is 2 meters long, 1.5 meters wide, and 1 meter tall. What is the volume of the container?
Your solution:
A cylindrical water tank has a radius of 3 meters and a height of 8 meters. Calculate the volume of the tank.
Your solution: