04 4 a.m數 (26分到)－航空百大

標題:

04 4 a.m數 (26分到)

發問:

http://xs130.xs.to/xs130/08342/04__4615.jpg 我想問人點做呢題,, guide 下我做 thx 係msn 教我 add 呢個, kalkma@msn.com ============================= 我會延長發問時間, until 有人add了我之後講到我知就簡佢

最佳解答:

Sorry, I do not do MSN, but I can provide you with the answer. You only have to integrate a small element of size dxdy from x=0 to sqrt(R^2-y^2) and for y=0 to 2. R=3 for x^2+y^2=9 (a circle of radius 3) The element will make a volume of 2pi x (dxdy) when revolved around the y-axis. So the total volume is integral(y=0 to 2 integral(x=0 to sqrt(R^2-y^2) (2 pi x dx dy) ) ) = integral(y=0 to 2 [2 pi x^2 / 2] x=0 to sqrt(R^2-y^2) ) = integral(y=0 to 2 (pi (R^2-y^2) ) =[pi( R^2y - y^3/3) ] y=0 to 2 =pi (2R^2 - 2^3/3) =pi (2 3^2 - 2^3/3) =pi (18 - 8/3) =46pi/3

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