Volume and Surface Area Calculator (Prism, Cylinder, Cone, Pyramid)
🎯 Select Geometric Shape:
📦 Rectangular Prism
🥤 Cylinder
🏔️ Cone
🔺 Pyramid
📐 Volume and Surface Area Calculator for Geometric Shapes
Calculate volume and surface area of fundamental 3D shapes: rectangular prism, cylinder, cone, and pyramid. Enter the required parameters and get accurate results with detailed formulas.
🔍 Supported Shapes:
- Rectangular Prism - length, width, height
- Cylinder - base radius, height
- Cone - base radius, height
- Pyramid - base area, height
📝 Calculation Formulas:
Rectangular Prism:
• Volume: V = a × b × h
• Surface Area: S = 2(ab + ah + bh)
Cylinder:
• Volume: V = π × r² × h
• Surface Area: S = 2πr(r + h)
Cone:
• Volume: V = (1/3) × π × r² × h
• Surface Area: S = πr(r + l), where l = √(r² + h²)
Pyramid:
• Volume: V = (1/3) × A_base × h
• Surface Area: S = A_base + A_lateral
💡 Applications:
- Architecture and construction planning
- Engineering calculations
- Material estimation for projects
- School geometry problems
- 3D modeling and design
Frequently Asked Questions
What units of measurement should I use?
All linear dimensions should be in the same units (cm, m, ft, etc.). Volume results will be in cubic units, surface area in square units.
What is the slant height of a cone?
The slant height (l) is the distance from the apex of the cone to any point on the base circle. It's calculated using l = √(r² + h²).
How do I calculate the base area of a pyramid?
Base area depends on the shape: square - a², rectangle - a×b, triangle - (1/2)×a×h, circle - π×r².
Why is the volume of cone and pyramid divided by 3?
This is a mathematical fact: the volume of a cone or pyramid is always 1/3 of the volume of a cylinder or prism with the same base and height.
Can I use different units for different measurements?
No, all measurements must be in the same units. Convert all values to the same unit system before calculating.