Volumes of Revolution : ExamSolutions

Tutorial on volumes of revolution
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[@ExamSolutions_Maths]

Thanks for your comments

[@ExamSolutions_Maths]

sin^2(some angle) + cos^2(same angle) always = 1 Try it on your calculator. Say sin^2 (62)+cos^2(62) or sin^2(78) + cos^2(78) etc.

[@8PetrStejskal]

hello, why my calculator gives error back when putting 1/(tan(pi/6)) ??? thx

[@AK476056]

Your calculator is not in radians mode

[@RShahProductions]

Dem birds tweeting at the end!!

[@xBustedHeart]

so since the formula for about the x axis is pi x the integral of y² dx so for about the y axis it would by pi x the integral of x² dy. And in this case for finding the volume generated about the y axis the x must be made the subject of the formula, right?

[@ExamSolutions_Maths]

***** That's correct. Check this out www.examsolutions.net/maths-revision/core-maths/integration/applications/volume%20of%20revolution/y-axis/tutorial-1.php

[@ExamSolutions_Maths]

Look on my website for your module and then look under trig. identities. It is all explained there.

[@aldicoverdale5137]

I plugged the third equation from the end into my calculator and got 248.826713. but when I plugged the end equation which was just a simpler version of it I got 27.9? why is this so?

[@ExamSolutions_Maths]

For which board and module?

[@hafsaimtiaz5832]

A level edexcel

[@ExamSolutions_Maths]

Ah, the video for volumes about the x-axis is uploaded but about the y-axis is still to be made.

[@danielhiggins2009]

would you mind explaining how you got this cos2A=1-2sin^2A?
i read your comment above but have still got no clue.

[@oifsdhnjiocnsrtyuhjnj]

cos(2A)= cos (A+A).
The Double Angle formula states cos(A+B) = cos(A)cos(B) - sin(A)sin(B).
Hence cos(A+A) = cos(A)cos(A) - sin(A)sin(A).
We can simplify this to "cos^2(A) - sin^2(A)", and (since "cos^2(X) + sin^2(X) = 1"), we can substitute "cos^2(A)" as "1 - sin^2(A)".
This leads to "1 - sin^2(A) - sin^2(A)" which finally leads us to 1 - 2sin^2A.

[@MzVixen05]

Thank You So MUCH!!!

[@Bladebreak3r]

The question says the curve is "rotated through 2pi radians about the x-axis." What does that mean?

[@Kaizen-dy5ps]

Hello person from 10 years ago, do you know what this means now?

[@Bladebreak3r]

@@Kaizen-dy5ps unfortunately not. Ten years ago I was in school and now I've forgotten everything I ever learned, so I don't even know what radians means anymore

[@ExamSolutions_Maths]

That's what happens when you record a video at dusk! At least no dogs barking this time or a police car going up the road.

[@conorosullivan4081]

ty v much

[@RShahProductions]

Ahaha, you're an absolute legend! Dedicated!!

[@th2]

great vid

[@knight9451]

thanks

[@indudas2478]

how do you get -sinx from -2cos2x

[@ExamSolutions_Maths]

It is - sin 2x not - sin x