Volumes questions

[hanaacdr]

Gi could i please get some help on question 5 and 6
I keep getting it wrong
For question 5- i got 27
For question 6- i got 16

[jakesilove]

Gi could i please get some help on question 5 and 6
I keep getting it wrong
For question 5- i got 27
For question 6- i got 16(Image removed from quote.)

Been a bloody long time since I've had to think about shit like this. Let's give it a go.

So, think about what it actually looks like. We've got a circle, and right angled isosceles triangles sticking out of it. The base of each triangle is going to be 2 times to y value at the particular x value. There are loads of symmetries here; we could find the volume from 0 to 3, and double it, or 0 to 3 using just the positive x axis, then times it by four.

Now, the right angled triangle must have height equal to y (draw yourself a diagram if you're confused as to why!). So, each triangle will have area of a half base, times height, which will be y squared!

So, we have our general area function for the triangle (y^2). Then, we integrate that over the range (-3 to 3, or whatever you decide). We convert our ys to xs, and boom, we're done? Sorry I have to run off, but I'm sure Rui is halfway through an answer/already finished anyway.

[RuiAce]

I am only going to do Q5. Please post up your working for Q6 if you require further assistance.

[hanaacdr]

Been a bloody long time since I've had to think about shit like this. Let's give it a go.

So, think about what it actually looks like. We've got a circle, and right angled isosceles triangles sticking out of it. The base of each triangle is going to be 2 times to y value at the particular x value. There are loads of symmetries here; we could find the volume from 0 to 3, and double it, or 0 to 3 using just the positive x axis, then times it by four.

Now, the right angled triangle must have height equal to y (draw yourself a diagram if you're confused as to why!). So, each triangle will have area of a half base, times height, which will be y squared!

So, we have our general area function for the triangle (y^2). Then, we integrate that over the range (-3 to 3, or whatever you decide). We convert our ys to xs, and boom, we're done? Sorry I have to run off, but I'm sure Rui is halfway through an answer/already finished anyway.

Thank you so much!