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

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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 Sqrt[2] , 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 - Sqrt[2]/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 - Sqrt[2] ) 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