The Student Room Group

maths help

https://imgur.com/a/skD9efX
https://imgur.com/a/e45w2aY
stuck on 4b. In the answer they seem to find the volume of the curve on the right side with limits of 0 and 2 but why are they changing x^2 into 2y? and what im most confused about is what the volume is that they're finding, i thought it was always below the curve as shown here: https://imgur.com/a/cm1fOwU
but if not surely it would tend to infinity? if it is finding the volume below the curve, how can the volume of the entire shape be that add the volume generated by the cone (triangle)? so im mainly confused on what the first part of the answer is actually doing, mainly where if the area its ifnding is above the curve or below it, thank you
Original post by Gent2324
https://imgur.com/a/skD9efX
https://imgur.com/a/e45w2aY
stuck on 4b. In the answer they seem to find the volume of the curve on the right side with limits of 0 and 2 but why are they changing x^2 into 2y?


Because the curvy bit of the shape is the curve with equation y=12x2y = \dfrac{1}{2}x^2 which is precisely rewritten as 2y=x22y = x^2 hence the valid substitution.

and what im most confused about is what the volume is that they're finding, i thought it was always below the curve as shown here: https://imgur.com/a/cm1fOwU


Nope. If you imagine spinning the shaded region about the y-axis, that creates a 3D solid and its volume is the one we are finding. It even says it's rotated about the y-axis in the question.

but if not surely it would tend to infinity? if it is finding the volume below the curve, how can the volume of the entire shape be that add the volume generated by the cone (triangle)? so im mainly confused on what the first part of the answer is actually doing, mainly where if the area its ifnding is above the curve or below it, thank you


We are NOT finding any area of that curve! We are jumping straight to the volume of revolution of it about the y-axis. Read up on your notes about it if you still think you're finding something 'under' it.
Original post by RDKGames
Because the curvy bit of the shape is the curve with equation y=12x2y = \dfrac{1}{2}x^2 which is precisely rewritten as 2y=x22y = x^2 hence the valid substitution.



Nope. If you imagine spinning the shaded region about the y-axis, that creates a 3D solid and its volume is the one we are finding. It even says it's rotated about the y-axis in the question.



We are NOT finding any area of that curve! We are jumping straight to the volume of revolution of it about the y-axis. Read up on your notes about it if you still think you're finding something 'under' it.

ok so for the first part of the question where they get 4pi, what is that a volume of in terms of the diagram? if it was around the x axis would that change which volume is formed even if the numbers dont change?
Original post by Gent2324
ok so for the first part of the question where they get 4pi, what is that a volume of in terms of the diagram?


This area rotated around the y-axis.

https://i.imgur.com/ivoTVWy.png

if it was around the x axis would that change which volume is formed even if the numbers dont change?


Yes.
Volume of Revolution has been removed from A Level.... only in Further Maths now ?
Original post by the bear
Volume of Revolution has been removed from A Level.... only in Further Maths now ?


yep, some of the questions get fairly hard id say, definately amongst the hardest topics in cp1

Quick Reply

Latest