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# Volume through rotation of 360 watch

1. y= -5/7x + 60/7

lower limit = 5

upper limit = 12

I use the pi times (integral of y^2 WRS x and substituting upper and lower limits.

When I try this question, I get the integral of y^2 as 25/147x^3 - 600/98x^2 + 360/49x

I can tell this is wrong, and when I substitute in the limits, I get a negative number.

I do not want to use the volume of cone formula

What mistake am I making if you know and could you post your working out? I already know the answer but not how to get it. It's 175pi/3
2. One of your terms is incorrect.

We have

3. (Original post by Regret786)
y= -5/7x + 60/7

lower limit = 5

upper limit = 12

I use the pi times (integral of y^2 WRS x and substituting upper and lower limits.

When I try this question, I get the integral of y^2 as 25/147x^3 - 600/98x^2 + 360/49x

I can tell this is wrong, and when I substitute in the limits, I get a negative number.

I do not want to use the volume of cone formula

What mistake am I making if you know and could you post your working out? I already know the answer but not how to get it. It's 175pi/3
Check
4. (Original post by Regret786)
y= -5/7x + 60/7

lower limit = 5

upper limit = 12

I use the pi times (integral of y^2 WRS x and substituting upper and lower limits.

When I try this question, I get the integral of y^2 as 25/147x^3 - 600/98x^2 + 360/49x

I can tell this is wrong, and when I substitute in the limits, I get a negative number.

I do not want to use the volume of cone formula

What mistake am I making if you know and could you post your working out? I already know the answer but not how to get it. It's 175pi/3
I suspect your y^2 is wrong because the x term in your integral is.
You can make your life easier and less prone to errors if you factorise out the 5/7
This leads to 5/7(-x+12) and then V = pi x integral of [5/7(-x+12)]^2 = 25pi/49 x integral of (-x+12)^2 dx

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5. Yeah I got it now guys, thanks a lot.

I made a mistake squaring 60/7. I forgetfully wrote 360/49 instead of 3600/49.

I had been looking for my mistake for quite a while now, can't believe it was something so small.

Fixing the mistake gives the correct answer.

Thanks again
6. I am just curious, how can the problem even be solved without the axis of revolution being stated?

Peace.

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Updated: January 19, 2016
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