Volume of a Hemisphere Calculator
Calculate volume and surface area of a hemisphere using radius, diameter, or area measurements
Calculate Hemisphere Volume
Hemisphere Properties
Volume
Radius
Formulas Used
Volume: V = (2/3) × π × r³
Base Area: Ab = π × r²
Cap Area: Ac = 2 × π × r²
Total Surface Area: A = 3 × π × r²
Surface to Volume Ratio: A/V = 9/(2r)
Example Calculation
Basketball Hemisphere Example
Problem: A basketball has a radius of 12 cm. What is the volume of one hemisphere?
Given: Radius (r) = 12 cm
Solution
Step 1: Apply hemisphere volume formula
V = (2/3) × π × r³
Step 2: Substitute values
V = (2/3) × π × (12)³
V = (2/3) × π × 1728
V = (2/3) × 5428.67
V = 3619.11 cm³
Hemisphere Properties
Half Sphere
A hemisphere is exactly half of a complete sphere
Curved + Flat Surface
Has both curved surface and circular base
Total Surface Area
Sum of curved surface + base area
Quick Formulas
Real-World Applications
Earth's hemispheres (Northern/Southern)
Architectural domes and structures
Sports balls and equipment
Bowl and container design
Scientific apparatus and tools
Understanding Hemisphere Volume and Surface Area
What is a Hemisphere?
A hemisphere is exactly half of a sphere, divided by a plane passing through its center. The word comes from the Greek "hemi" (half) and Latin "sphaera" (globe). It consists of a curved surface (hemisphere cap) and a flat circular base.
Volume Formula Derivation
Since a hemisphere is half of a sphere, its volume is simply half the sphere's volume:
Sphere volume: Vsphere = (4/3)πr³
Hemisphere volume: V = Vsphere/2 = (2/3)πr³
Surface Area Components
Unlike a sphere, a hemisphere has additional surface area from its flat base:
- •Base area: πr² (flat circular surface)
- •Cap area: 2πr² (curved surface)
- •Total area: 3πr² (base + cap)
Key Insight: A hemisphere's total surface area is greater than half a sphere's surface area due to the additional base area.
Alternative Calculation Methods
From Diameter
When diameter is known:
V = (π/12) × d³
From Base Area
When base area is known:
V = (2/3) × √(Ab³/π)
From Total Area
When total surface area is known:
V = (2/9) × A³⁄²/(3π)