### What is the total area of the figure below?

This question aims to find the area of the given Figure 1 with two semi-circles and a parallelogram attached together. The question is based on the geometry of 2D shapes that are circles and a parallelogram. The area of the parallelogram can be calculated by taking the product of its height and base sides. The […]

### Describe in words the surface whose equation is given. r = 6

The aim of this question is to infer/visualize the shapes/surfaces constructed from a given mathematical function using prior knowledge of standard functions. The standard equation of a circle in two-dimensional plane is given by: Read moreIdentify the surface whose equation is given. ρ=sinθsinØ[ x^2 + y^2 = r^2 … … … ( 1 )] The […]

### A uniform lead sphere and a uniform aluminum sphere have the same mass. What is the ratio of the radius of the aluminum sphere to the radius of the lead sphere?

The aim of this question is to learn the volume of a sphere and the density of different materials. If the radius r is known, the volume V of a sphere is given by: Read moreIdentify the surface whose equation is given. ρ=sinθsinØ[ V = dfrac{ 4 }{ 3 } pi r^3 … … … (1) ] […]

### Identify the surface whose equation is given. ρ=sinθsinØ

The aim of this question is to find the surface corresponding to the Spherical Coordinates $p=sintheta sinphi$ by utilizing the Cartesian Coordinate system and Equation of Sphere. First, we will explain the concept of Sphere, its Equation, and its Coordinates in the Cartesian Coordinate System. Read moreA uniform lead sphere and a uniform aluminum sphere […]