Circle and Sphere Formulas, Definitions, Example Calculation

Circle Formulas

Circle Diameter (D)

The diameter of a circle is the distance across the circle through its center, or twice the radius.

Formula: D = 2r

Example Calculation: If radius (r) = 5 units

D = 2 * 5 = 10 units

---

Circle Calculator

---

Circle Area (A)

The area of a circle is the total space enclosed by the circle's circumference.

Formula: A = πr²

Example Calculation: If radius (r) = 5 units

A = π * 5² = 25π square units

Circumference of a Circle (C)

The circumference of a circle is the distance around the circle's boundary.

Formula: C = 2πr

Example Calculation: If radius (r) = 7 units

C = 2π * 7 = 14π units

Arc Length (L)

The arc length of a circle is the distance along the portion of the circle's circumference.

Formula: L = (C / 360) * θ

Example Calculation: If circumference (C) = 10 units and central angle (θ) = 45 degrees

L = (10 / 360) * 45 = 1.25 units

Sector Area (A)

The sector area of a circle is the region enclosed by an arc and two radii.

Formula: A = (C / 360) * πr²

Example Calculation: If circumference (C) = 10 units and radius (r) = 3 units

A = (10 / 360) * π * 3² = 0.2618π square units

Sphere Formulas

---

Sphere Calculator

---

Surface Area of a Sphere (A)

The surface area of a sphere is the total area covered by the sphere's surface.

Formula: A = 4πr²

Example Calculation: If radius (r) = 3 units

A = 4π * 3² = 36π square units

Volume of a Sphere (V)

The volume of a sphere is the amount of space enclosed by the sphere's surface.

Formula: V = (4/3)πr³

Example Calculation: If radius (r) = 4 units

V = (4/3)π * 4³ = (4/3)π * 64 = 256π cubic units

Surface Area of Hemisphere (A)

The surface area of a hemisphere is the total area of its curved surface.

Formula: A = 2πr²

Example Calculation: If radius (r) = 3 units

A = 2π * 3² = 18π square units

Volume of Hemisphere (V)

The volume of a hemisphere is half the volume of a sphere with the same radius.

Formula: V = (2/3)πr³

Example Calculation: If radius (r) = 4 units

V = (2/3)π * 4³ = (2/3)π * 64 = 128π cubic units

Segment Volume (V)

The volume of a spherical segment is the volume of a sphere cut by a plane.

Formula: V = (1/6)πh(3a² + h²)

Example Calculation: If height (h) = 6 units and radius of the base (a) = 5 units

V = (1/6)π * 6 * (3 * 5² + 6²) = 210π cubic units