Rotated - Calculus - Solved Exam, Exams of Calculus

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MATH 106 Exam 2 Review October 27, 2004 1. Write an integral equal to the volume of a cone of radius 7 feet and height 13 feet. Sli horieo rtally - +otal vol & sha & ar Sh cf C- z vol aw thy h ne w(28) Bh ve ah 2 2. Consider the region defined by y = a, x = 0, y = 0, and x = 9. Write an integral equal to the volume generated if this region is rotated about (a) the z-axis wal & she x Tr AY = Ty aK = W (Sr) OK HK AK 4 rey Artal = J wxdx ax 4 vol ° slie verttealy i 2 yet (o) thelmer=-1 Vol of sit @ Th (cule rece) “y —11( Taner radivey ay ‘es x TCte)"ay - T(X+)*ay (naps ~ “y 4 4otal SMe hovigoutally vol TT: 100 4Y — T(4>+) ay 3. Compute the arclength of the curve y = 2°/* between z = 0 and « = 3/4. (Note: 9:30 and 1:10 sections should omit this question.] x= 4H 3a | 527A = | & See. AY length = f t+ [eta dy os 2 we: ado = re) ~ K=oe 4 = § (+x ax 34 S @ Ba Seay’ | w= 4 4x dw = Say 3. aa ( (42) *- 1) 4. A cylindrical tank of radius 4 feet and length 10 feet Is buried on its side 3 feet below ground. If the tank is filled to a height of 6 feet. with water (62.4 pounds per cubic foot), write an integral equal to nM M the work done in pumping all the water to the surface. h \suct ———— At total wovk = sire horially : re 4624 +2 Jon=wRCrh) dh Ls 4 ° SLY 5 h oly 2 uw Lu ek)” vol a slra & lOwdsh 4? =(Z) +C fe weight of sla A 624U5h \e= we 416- Bh th Work on site %& 624W- dW(lI-h) 4(Bh- we) = uy> 2 Jerr = &