Finding the volume of a fishbowl by integration Created by: Justin Kenzie & Eleora Christy Performance task of mathematics Binus School Bekasi.

1. Volume of An Object
Using Calculus
Justin Kenzie & Eleora Christy
Performance
Task
Mathematics
HS11B

2. Calculus deals with topics like instantaneous rates of change, areas under curves, and
sequences and series. Under these topics, there is a concept of limit, which consists of
analyzing the behavior of a function at points ever closer to a particular point, but without
ever reaching that point. Calculus has two basic applications which are: differential calculus
and integral calculus.
In this presentation, we are going to look at an example problem of integral calculus which
will be used to find a volume of a fishbowl. With this example, the formula volume of
revolution through the x-axis is applied.
1
Prologue

3. Step 1
Put the picture in Desmos, And then make an outline.
2
Make the outline just like:

4. Step 1
Because our graph is not accurate to outline our picture, we decided to use two graphs.
3
It'll look like:

5. Step 3
4
Determine the boundaries of the 2 graphs.
We do this by:
Purple Graph Green Graph
This calculation tells us that for the first
quadrant, the two functions meet on x=3.95
and x=-3.95
The green function will be divided into two, the one in the
first and the other in the second quadrant. For the first
quadrant, its’ boundaries are 3.95 < x < 4.664. While for the
second quadrant, its’ boundaries are -4.664 < x< -3.95.

6. Step 3
5
With these boundaries in mind, this is what the graph looks like:

7. Step 4
6
Use the solid of revolution by x-axis formula:
The formula for the volume of the object:
+ +

8. Step 4
7
Find y^2 for both function:
Green graph
Purple graph

9. Step 4
8
Integrate the functions:

10. Step 4
9
Integrate the functions:

11. Step 5
10
Find the total volume:
131.5π + 1.5π + 1.5π
134.5π cu

12. Thank you
for reading!
Justin Kenzie & Eleora Christy
Performance
Task
Mathematics
HS11B