Surface Areas and Volumes
Calculating surface areas and volumes of 3D shapes
Interactive Surface Areas and Volumes Visualization
Welcome to the Surface Areas and Volumes Explorer
This interactive visualization helps you understand how to calculate surface area and volume for different 3D shapes. Explore cubes, prisms, cylinders, spheres, cones, and pyramids with their formulas and calculations. The 3D shapes rotate automatically for better visualization.
What you can explore:
- Surface Area - Total area of all faces (square units)
- Volume - Space inside a 3D shape (cubic units)
- 3D Shapes - True 3D visualization with Three.js
- Formulas - Mathematical formulas for each shape
How to Use This Visualization
Interactive Features:
- • Select Shape - Choose from 6 different 3D shapes
- • Adjust Dimensions - Change size with sliders
- • Auto Rotation - Shapes rotate automatically
- • View Formulas - See surface area and volume formulas
What You'll See:
- • 3D Shape - True 3D rendering with lighting
- • Grid & Axes - Reference grid and coordinate axes
- • Surface Area & Volume - Calculated values
- • Formulas & Steps - How calculations are performed
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Surface Area
150.00 square units
SA = 6s²
6 × 5² = 6 × 25 = 150.00
Volume
125.00 cubic units
V = s³
5³ = 125 = 125.00
Understanding Surface Area
Surface Area is the total area of all faces/surfaces of a 3D shape.
It's measured in square units (e.g., cm², m², ft²).
To find surface area, calculate the area of each face and add them together.
Examples: Cube = 6s², Cylinder = 2πr² + 2πrh
Understanding Volume
Volume is the amount of space inside a 3D shape.
It's measured in cubic units (e.g., cm³, m³, ft³).
Volume represents how much a container can hold or how much space an object occupies.
Examples: Cube = s³, Cylinder = πr²h, Sphere = (4/3)πr³
Common Surface Area and Volume Formulas
Cube:
SA = 6s², V = s³
Rectangular Prism:
SA = 2(lw + lh + wh), V = lwh
Cylinder:
SA = 2πr² + 2πrh, V = πr²h
Sphere:
SA = 4πr², V = (4/3)πr³
Cone:
SA = πr² + πrl, V = (1/3)πr²h
Pyramid:
SA = base + lateral, V = (1/3)Bh
Lessons
Individual learning units
Lessons coming soon