Volume Of Hemisphere
Calculate hemisphere volume instantly from radius with V = (2/3)pir^3. Free online 3D geometry calculator for domes, bowls, igloos, and half-sphere shapes with interactive chart.
About This Calculator
This Volume Of Hemisphere Calculator computes the volume of a hemisphere -- exactly half of a sphere -- from its radius. Enter the radius to get the volume in cubic units, along with the equivalent full sphere volume and a visual chart showing volume as a function of radius.
The calculator uses the formula V = (2/3)pir^3, which is half of the sphere volume formula (4/3)pir^3. A hemisphere consists of the curved dome surface and a flat circular base.
Key formulas:
- Hemisphere volume: V = (2/3)pir^3
- Full sphere volume: V = (4/3)pir^3 (exactly double the hemisphere)
- Curved surface area: 2pir^2
- Total surface area (with base): 3pir^2
The chart plots hemisphere volume across different radius values, helping you visualize how volume grows exponentially with radius.
Frequently Asked Questions
What is the formula for hemisphere volume?
The formula for the volume of a hemisphere is V = (2/3)pir^3, where r is the radius. Since a hemisphere is exactly half of a sphere (sphere volume = (4/3)pir^3), the hemisphere volume is simply (1/2) x (4/3)pir^3 = (2/3)pir^3.
How is hemisphere volume different from sphere volume?
A hemisphere has exactly half the volume of a full sphere with the same radius. Sphere volume = (4/3)pir^3, while hemisphere volume = (2/3)pir^3. So if you know the sphere volume, simply divide by 2 to get the hemisphere volume.
What is the volume of a hemisphere with radius 5?
Using V = (2/3)pir^3: V = (2/3) x pi x 5^3 = (2/3) x pi x 125 = (2/3) x 392.7 = 261.8 cubic units. The corresponding full sphere volume would be 523.6 cubic units.
What is the surface area of a hemisphere?
The total surface area of a hemisphere includes both the curved surface and the flat circular base. The curved surface area is 2pir^2 (half of the sphere's 4pir^2), and the base area is pir^2. Total surface area = 2pir^2 + pir^2 = 3pir^2.
What are real-world examples of hemispheres?
Real-world examples include domes (like the US Capitol dome, St. Peter's Basilica, and the Taj Mahal dome), half-ball decorations, bowls and salad bowls, igloos, observatory domes, planetary science (Earth's northern and southern hemispheres), and even half-sphere aquarium tanks.
Is this tool free to use?
Yes, all calculators on Calculy are completely free to use with no registration required. You can also share your calculation results via URL.
What is half a sphere called?
A hemisphere. The word comes from Greek "hemi" meaning "half" and Latin "shaera" meaning "globe". The Earth is divided into northern and southern hemispheres, and also eastern and western hemispheres.
How many faces does a hemisphere have?
A hemisphere has one flat face (the circular base) and one curved surface (the dome). It has one circular edge where the base meets the curved surface, and no vertices.