(a) When standing on one of its circular ends, a typical Bordeaux wine barrel has

height 94cm. The diameter of the barrel at the widest point is 70cm. When the

barrel is standing in this way, the curved edge of the vertical cross section (through

the centre of the barrel) is a parabola whose derviative is 2

2/275x, where x is the

vertical distance from the centre of the barrel. Assuming that 1 litre = 1000cm3,

find the volume of wine that the barrel holds.

[(b) Evaluate the validity of your answer by calculating the volume of a more funda-

mental solid of similar dimensions.

I thought as we are talking about a barrel the volume is in this case Volume(barrel)=h*Pi*(2r1^2 + r2^2) / 3

Also though as y`= 2/275x then y=x^2/275

hence the volume of the barrel must be the Pi*Integral of y^2 dx( formula)

so Pi*integral of (x^2/275)^2 dx must be equal to =h*Pi*(2r1^2 + r2^2) / 3 but that wasnt the case, I couldnt find r2 but I claimed that it was

r1/2 but in the end I got that(finding volume with integration formula) Pi*(x^5/378125)+C= 271350,975(finding volume barrel formula) I AM NOT SURE WHAT TO DO NEXT...=(