Find the volume of the described solid. The solid lies between planes perpendicu

Question

Find the volume of the described solid. The solid lies between planes perpendicular to the x-axis at x from the parabola y xto the parabola y 32-x2 256 4 and x-1. The cross sections perpendicular to the x-axis are circular disks whose diameters run 3192 16384 QUESTION 14 Solve the problem. water tank is formed bv revolving the curve v = 2x4 about the v-aus. Water drains from the tank through a small hole in the boer m of the tank At rate does the water level. y, tall? Use Torricelli's Law: dv/dt -mfy tat

Explanation / Answer

13)

diameter of disk ,d= (32-x2)-x2

diameter of disk ,d= (32-2x2)

radius of disk ,r= d/2

radius of disk ,r= (32-2x2)/2

radius of disk ,r= (16-x2)

area of cross section ,A= r2

A= (16-x2)2

A= (256-32x2+x4)

volume of solid =[-4 to 4](256-32x2+x4)dx

volume of solid =|[-4 to 4](256x-(32/3)x3+(1/5)x5)

volume of solid =(256(4)-(32/3)(4)3+(1/5)(4)5) -(256(-4)-(32/3)(-4)3+(1/5)(-4)5)

volume of solid =16384/15

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14)

y=(2x4)

=>x4=(y/2)

=>x=(y/2)1/4

radius of disk =(y/2)1/4

by disk method ,

volume of solid ,V= ((y/2)1/4)2 dy

=>dV/dt= ((y/2)1/4)2 *(dy/dt)

=>dV/dt= (/2)y *(dy/dt)

=>-my= (/2)y *(dy/dt)

=>-m= (/2) *(dy/dt)

=>dy/dt=-(m2)/

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