Which if the following is true about the diameter of a sphere

Answer 1

The diameter of a sphere has the following characteristics:

1. Definition: The diameter of a sphere is the longest straight line that can be drawn through the center of the sphere, connecting two points on its surface.

2. Relation to Radius: The diameter is twice the length of the radius (d = 2r), where the radius is the distance from the center of the sphere to any point on its surface.

3. Constant at All Points: No matter where you measure it, as long as the line passes through the center, the diameter of a given sphere will always be the same length.

4. Central Axis: The diameter represents the central axis of the sphere around which rotational symmetry exists.

5. Volume and Surface Area: The diameter of a sphere is used in the formulas for calculating the volume (V = 4/3 * π * r^3) and the surface area (A = 4 * π * r^2) of the sphere. These formulas can also be expressed in terms of diameter using d = 2r; thus, volume can be written as V = 1/6 * π * d^3 and surface area as A = π * d^2.

6. Geometric Property: The diameter of a sphere, like other geometric dimensions, is a linear measure, which means it is a one-dimensional measure of length, unlike the sphere's volume and surface area, which are three- and two-dimensional measures respectively.

7. Circular Cross-Sections: Any cross-section of a sphere made by slicing it with a plane that passes through its center will be a circle with a diameter equal to the diameter of the sphere.

The concept of a sphere's diameter is fundamental to the geometry of spheres and is used extensively in mathematical equations relating to spheres and in practical applications such as calculating the size of spherical objects.