[WSS19] Calculate the volume, surface area, circumference and area

[abegadalla (Abraham Gadalla)]

#Surface Area and Volume of an Egg

#Write parametric equations to draw an egg shaped figure

Drawing the egg with both Cartesian and Parametric equations.

• First Using Cartesian Equations

   ClearAll["Global`*"]; Clear[a];
  

#Calculate the area and the circumference of an egg-shaped figure.

The egg - shaped figure is drawn using a Piecewise Function as follows :

1. A semicircle with radius = “a” , center at origin and angle between
   -[Pi]/2, [Pi]/2.
2. A sector with radius = 2 a , center at {0, - a) and angle between [Pi]/2 and 3[Pi]/4.
3. A sector with radius = 2 a -a Sqrt2 , center at {-a, 0) and angle between3 [Pi]/4 and 5
   [Pi]/4.
4. A sector with radius = 2 a , center at {0, a) and angle between 5[Pi]/4 and 3[Pi]/2.

Calculus students are asked to calculate the volume and the surface area of the figure based on the assigned value of the main radius a.

The circumference of the figure = (3 - Sqrt2/2) [Pi] a cm, which is approximately = 2.293 [Pi] a cm.

The circumference is calculated as follows : Twice the upper curve =
2 { quarter circle with radius a + Arc of a sector whose radius = 2 a +
Arc of a sector with radius (2 - Sqrt2 ) a }

#Project Calculate the volume, surface area, circumference and area of the egg shaped figure

#Project Calculate the volume, surface area, circumference and area of the egg shaped figure