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Written Assignment 1Answer all assigned exercises, and show all work. Each exercise is worth 5 points.Section 5.22.Find the volume of the solid with cross-sectional area A(x).0.01( )10, 010xA xex( )baVA x dx100.01010()xedx100.01100.01001010000.01xxee0.01(10)0.01(0)0.101000100010001000eeee1105.171000105.17105.17V6.Find the volume of a pyramid of height 160 feet that has a square base of side 300 feet. These dimensions are half those of the pyramid in example 2.1. How does the volume compare?Height=160ftSquare base of side=300ftx=height above groundAt x=0, cross-section= 300At x=160,cross-section=0f(x)=side length of square cross at height xf(0)=600, f(160)=0, f(x)=linear functionslope(m)3000300016016015( )3008f xxThe cross-sectional area is simply the square of f(x) so that we have:WA 1, p. 1
16016020015( )(300)8xA x dxdxEvaluate the integral by substitution153008uxso that 158dudx1600220300158(300)815Vdxu du30030033320088(300)(0)1515333uVu du389000000154,800,000VVft3338,400,00084,800,0001ftftThe new pyramid is 1/8 the volume of the original pyramid in example 2.110.A dome “twice as big” as that of exercise 9 (see text) has outline 2120120xyfor120120x(units of feet). Find its volume.12020Vx dx1200120 120y dy120222022312012012012012022240120120120222yyV=864000π ft312.A pottery jar has circular cross sections of radius 24sinxinches for 02 .xSketch a picture of the jar and compute its volume.( )baVA x dxWA 1, p. 2
2204sin2xdx220168sinsin2222sin 200sin 016(2)16cos16(0)16cos222222xxdx3216001600V=33π3inch318.Compute the volume of the solid formed by revolving the region bounded by2212,4yxyx about (a) the x-axis; (b) y=4Intersection of the curves: y2 = y1WA 1, p. 3 y =x2y = 4-x2x-axisy=4
222244222xxxxx(a)Revolved about the x-axis2222222222()(4)()oiVr dxrrdxxxdx2244233232(168)()88(2 )8(2 )1616216(2)333xxxdxxx962322336423V(b) Revolved about y = 42222