This week we learned 7.3. We are close to the end of the Calculus 1!!!
We learned how to find the volume of disks and washers.
There are two formulas in terms of x and y for each. If I memorize the formula, I won't be in any trouble.
But, there's one part that might be confusing: a radius.
Radii can be a function itself, but sometimes can be a function subtracted by another function.
The example is the picture at the bottom! But, if I look into it closely, I can easily find the radius!
Another tricky question was on #5 the chapter 7.3 quiz. There's a bounded area and we needed to find the volume of the area rotated around x=-1. Firstly, I did it in the same way I did around y-axis. And, I thought I got the right answer. But, a question arose. Why did Mr.Cresswell rotate it around x=-1? And, I found that I was supposed to add 1 to each function before being squared (because the short and long radii included 1 unit.) - hopefully, that sentence makes sense :)
After that, when I compared the two answers, there's some difference, but it was not like a simple number(such as fraction.), while I expected the second one would be larger by 8 than the first one. (Because the rectangle had a width of 2 and a height of 4.) I wondered why my guess was wrong. I found out I thought of the shape as 2-dimension shape. In reality, it is 3d shape, so I can't just add the area of the rectangle.
Overall, my participation was good. I did homework well and filled out CCC. This weekend, I am gonna rest! Have a great weekend!
We learned how to find the volume of disks and washers.
There are two formulas in terms of x and y for each. If I memorize the formula, I won't be in any trouble.
But, there's one part that might be confusing: a radius.
Radii can be a function itself, but sometimes can be a function subtracted by another function.
The example is the picture at the bottom! But, if I look into it closely, I can easily find the radius!
Another tricky question was on #5 the chapter 7.3 quiz. There's a bounded area and we needed to find the volume of the area rotated around x=-1. Firstly, I did it in the same way I did around y-axis. And, I thought I got the right answer. But, a question arose. Why did Mr.Cresswell rotate it around x=-1? And, I found that I was supposed to add 1 to each function before being squared (because the short and long radii included 1 unit.) - hopefully, that sentence makes sense :)
After that, when I compared the two answers, there's some difference, but it was not like a simple number(such as fraction.), while I expected the second one would be larger by 8 than the first one. (Because the rectangle had a width of 2 and a height of 4.) I wondered why my guess was wrong. I found out I thought of the shape as 2-dimension shape. In reality, it is 3d shape, so I can't just add the area of the rectangle.
Overall, my participation was good. I did homework well and filled out CCC. This weekend, I am gonna rest! Have a great weekend!