Dayv O. answered • 12/08/20
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Using disks with x(y) =r and use dy for integration.
x(y)=9*(y/6)(2/3), want to integrate pi*x2*dy
that is integrate (pi*81/6(4/3)*y(4/3)*dy and evaluate y=0 to y=750 (=6*52)
the result I come up with is ((pi*81*3)/7*6(4/3))*y(7/3) evaluated from y=0 to y=750
=3.57*108
Dayv O.
yikes, and apology -- i calculated volume not surface area. you probably know the formula, I will see if I can figure out.
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12/08/20
Dayv O.
new answer, surface area = (5^4)*(18^2)*pi left all in t variable, integrated with dt. for radius used x(t) ---for ds used square root of (dx/dt)^2+(dy/dt)^2)*dt---- had to integrate 2*pi*x(t)*ds from t=0 to t=5.----came up with (18^2)*pi times the integral of (t^4)*(t^2+1)^(1/2) --- to solve that integral, substitute t=sinh(theata). ---- the result is sinh^5(theta)/5. when t=5, theta = sinh^-1(5). --Sorry about volume mis-step. comment back if you need more help.
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12/08/20
Dayv O.
750=6*5^312/08/20