Finding The Volume of a Fishbowl By Integration.pdf
- 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