Finding volume of Easter Egg by integration created by: Sakti and Malvien Performance task of mathematics Binus School Bekasi.

1. HOW TO FIND THE
VOLUME OF AN
EASTER EGG BY
INTEGRATION
A Q U I C K I N F O R M A T I O N G U I D E
Created by Sakti and Malvien

2. Using Desmos
A G R A P H I N G W E B S I T E
We can use desmos.com to make curves from
an equation.
By lining up 2 curves from the same function,
we can almost replicate the shape of the egg.
From here, we can calculate the volume from
just these very curves.

3. Use of equation
By using the equation above, we can add a slider in the website
which can be used to shape the curve however we want.

4. Calculating the Volume
B y u s i n g t h e f o r m u l a
V = π ( ∫ f ( y ) ² d y )
We can calculate the volume of the egg by using the
formula above.
We only need to calculate half of the shape itself because
we are going to be rotating it by the y-axis. Which means
that we only need one curve to calculate the volume.
We can use y-values formed from the x-axis and the upper
intersection of the 2 curves to be the boundaries for our
calculation.

5. x = -0.3 (y - 2)² + 2 = 0
-0.3 (y² - 4y + 4) + 2 = 0
-0.3y² + 1.2y - 1.2 + 2 = 0
-3/10y² + 6/5y + 0.8 = 0
-3y² + 12y + 8 = 0
y = (-(-12) + √((-12)² - 4 ⋅ 3 ⋅ (-8))) / (2 ⋅ 3)
y = (12 +/- 4√(15)) / 6
y1 = 4.58
y2 = - 0.58
V = π (∫ f(y)² dy)
V = π ( ∫⁴ ⁵⁸ (-0.3y² + 1.2y + 0.8)² dy)
V = π ( ∫⁴ ⁵⁸ (9/100y⁴ + 24/25y² + 16/25 - 18/25y³ + 48/25y) dy)
V = π (9y⁵/500 + 8/25y³ + 16/25y - 9y⁴/50 + 24/25y²) | ⁴ ⁵⁸
V = π (9(4.58)⁵/500 + 8/25(4.58)³ + 16/25(4.58) - 9(4.58)⁴/50 + 24/25(4.58)²) - (0)
V = 11π cubic units
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Calculations
HOW ARE THE CALCULATIONS TO
GET THE VOLUME
In here, our curve has the equation x = -0.3 (y-2)² + 2
So we will use that equation for the calculations.

6. Conclusion
So that is how you can get a volume from
an irregular shape. Not so bad right? The
use of integration has proven quite handy!
Use Desmos and find the volume in the
area of a curve. Just like that you'll be
able to calculate the volume of whatever
object you want to.

7. Thank You
For viewing!