Volume & Surface Area Explorer
Interactive 3D Shape Calculator. Visualize dimensions and calculate Volume & Surface Area for Cylinders, Spheres, and Cones.
Dive into 3D Geometry! Adjust the **Radius** and **Height** to see how Volume and Surface Area change for common shapes.
✓ Interactive Models✓ Real-time Calc✓ Cylinder, Sphere, Cone✓ Mensuration Formulas
Shape Dimensions
5
10
3D Preview
Calculations
Volume
785.40units³
Surface Area
471.24units²
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What is Volume & Surface Area Explorer?
Volume vs Surface Area
- Volume: The amount of space inside a 3D object. Think of how much water it can hold. Measured in cubic units ($u^3$).
- Surface Area: The total area of all outer surfaces. Think of how much paint you need to cover it. Measured in square units ($u^2$).
Formula & Calculation
Cylinder
Like a soda can.
V = πr²h
A = 2πr(r+h)
A = 2πr(r+h)
Sphere
Like a basketball.
V = 4/3 πr³
A = 4πr²
A = 4πr²
Cone
Like an ice cream cone.
V = 1/3 πr²h
A = πr(r + s)*
A = πr(r + s)*
*s = slant height
Example Calculation
Sphere vs Cylinder Volume
Archimedes proved that a sphere inscribed in a cylinder has exactly 2/3 of the cylinder's volume.
- Try Cylinder: r=3, h=6 (because h=2r)
- Try Sphere: r=3
- Calculate ratio of volumes!
Frequently Asked Questions
What is 's' in the Cone formula?
It stands for **slant height**—the distance from the tip of the cone down the side to the edge of the base. It creates a right triangle where $s = \sqrt{r^2 + h^2}$.