Write the area A of a circle as a function of its circumference C.

The purpose of this question is to explain the geometry of the circle, understand how to calculate the circumference and the area of the circle, and learn how the different formulas of the circle relate to each other. The assemblage of points that are at a specified distance $r$ from the center of the circle […]

Find an equation for the plane consisting of all points that are equidistant from the points (1,0,-2) and (3,4,0).

This problem aims to familiarize us with geometrical calculations. The concept required to solve this problem is the distance formula in 3-dimensional space, and some square and cubic algebraic formulas. The formula for distance states that the distance between two points in xyz-space is the sum of the squares of the differences between similar xyz coordinates under a square root. Let’s say we have points: [ P_1 = (x_1,y_1,z_1)space andspace P_2 = (x_2,y_2,z_2)] The […]

If the atomic radius of lead is 0.175 nm, calculate the volume of its unit cell in cubic meters.

The aim of this question is to calculate the volume of a unit cell, giving due attention to the lettuce structure of the given metal. The uniform spatial arrangement scheme of atoms, molecules, and/or ions is called crystal structure. The overall crystal structure can be divided into smaller basic elements that can be spatially repeated to […]

Find all polar coordinates of point p = (6, 31°).

This question aims to find the polar coordinates of a point P that is equal to (6, 31°). P is a point on the xy plane. x and y axis are known as the polar axis, while the origin of the xy plane is called the pole. The point P is represented in the form […]

Find the equation of the sphere centered at (-4, 1, 4) with radius 3. Give an equation which describes the intersection of this sphere with the plane z = 6.

This question aims to find the equation of the sphere centered at (-4, 1, 4) in 3D coordinates and also an equation to describe the intersection of this sphere with a plane z=6. The question is based on the concepts of a solid geometry. Solid geometry is the part of mathematics geometry that deals with solid […]