Sphere, Cone & Cylinder Calculator
How It Works
This sphere, cone & cylinder calculator uses established formulas to provide accurate results.
The basic rule:
- V(sphere) = (4/3)πr³
- V(cone) = (1/3)πr²h
- V(cylinder) = πr²h
- SA(sphere) = 4πr²
- SA(cylinder) = 2πr(r + h)
Results are estimates. Consult a professional for critical decisions.
Frequently Asked Questions
How do you calculate the volume of a sphere?
The volume of a sphere is V = (4/3)πr³. Cube the radius, multiply by π, then multiply by 4/3. For example, a sphere with radius 5 has volume (4/3)π(125) ≈ 523.6 cubic units.
What is the slant height of a cone?
The slant height is the distance from the tip of the cone to any point on the edge of the base circle. It can be found using the Pythagorean theorem: slant = √(r² + h²), where r is the radius and h is the height.
How are cone and cylinder volumes related?
A cone's volume is exactly one-third of a cylinder with the same radius and height. V(cone) = ⅓ × V(cylinder) = ⅓πr²h.
Does the sphere formula use height?
No. A sphere is defined entirely by its radius. The volume formula V = (4/3)πr³ and surface area formula SA = 4πr² both depend only on the radius.