CalculateY
Quick Answer
A sphere with radius 5 has a volume of approximately 523.60 cubic units. A cylinder with radius 3 and height 10 has a volume of approximately 282.74 cubic units.
Common Examples
| Input | Result |
|---|---|
| Cube: side 4 | 64 cubic units |
| Sphere: radius 5 | 523.60 cubic units |
| Cylinder: radius 3, height 10 | 282.74 cubic units |
| Cone: radius 4, height 9 | 150.80 cubic units |
How It Works
Cube: V = s³
Multiply the side length by itself three times. For a cube with side length 5, the volume is 125 cubic units.
Rectangular Prism: V = l × w × h
Multiply the length by the width by the height. For a prism measuring 4 × 3 × 2, the volume is 24 cubic units.
Sphere: V = (4/3) × π × r³
Multiply four-thirds by π (approximately 3.14159) by the radius cubed. For a sphere with radius 5, the volume is approximately 523.60 cubic units.
Cylinder: V = π × r² × h
Multiply π by the radius squared by the height. This is the area of the circular base multiplied by the height.
Cone: V = (1/3) × π × r² × h
Multiply one-third by π by the radius squared by the height. A cone has exactly one-third the volume of a cylinder with the same base and height.
Worked Example
For a sphere with radius 5: Volume = (4/3) × pi × 5³ = (4/3) × pi × 125 = 500pi/3 ≈ 523.60 cubic units. For a cylinder with radius 3 and height 10: Volume = pi × 3² × 10 = 90pi ≈ 282.74 cubic units. A cone with the same dimensions has 1/3 the volume: (1/3) × 90pi ≈ 94.25 cubic units.