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 12 Genuine CROSS Porous Point Black Fine Refills 8444 $16.20 Time Remaining: 6d 17h 42m Buy It Now for only: $16.20 |
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 New Executive Roller Ball Pen Pencil Set Storage Case Cross Refills Black Ink $7.95 Time Remaining: 25d 9h 39m Buy It Now for only: $7.95 |
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 20 Black Gel Ink Cross Style Ion Refills Fine Point $13.25 Time Remaining: 21d 18h 31m Buy It Now for only: $13.25 |
 2 MONTEVERDE BLUE BLACK FINE ROLLERBALL REFILLS FIT CROSS $6.49 Time Remaining: 8d 16h 13m Buy It Now for only: $6.49 |
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 4 CROSS BALLPOINT REFILLS BLUE BROAD POINT NEW IN PACKS 2 PACKS $9.95 Time Remaining: 2d 10h 6m |
 Red Cross style Refills $8.49 Time Remaining: 12d 16h 29m Buy It Now for only: $8.49 |
 5 CROSS BALLPOINT REFILLS BLACK MED POINT Free SHIPPING $7.49 Time Remaining: 11d 19h Buy It Now for only: $7.49 |
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 2 CROSS BP REFILLS BLUE MED SOFTROLLER BY MONTEVERDE $5.50 Time Remaining: 20d 3h 42m Buy It Now for only: $5.50 |
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 Lot of 4 Vintage AT CROSS Rolling Ball Refills Rollerball $4.99 Time Remaining: 24d 9h 26m Buy It Now for only: $4.99 |
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 4 CROSS BALLPOINT REFILLS BLUE FINE POINT NEW IN PACKS 2 PACKS $9.95 Time Remaining: 2d 20h 2m |
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 8 CROSS Blue Fine PEN BALLPOINT REFILLS Genuine $10.97 Time Remaining: 15h 17m Buy It Now for only: $10.97 |
 6 CROSS GENUINE Refills SELECTIP RBall Pens BLUE $18.83 Time Remaining: 15h 17m Buy It Now for only: $18.83 |
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 2 CROSS 8753 05mm 09mm PENCIL ERASER 5 PACK NEW $8.97 Time Remaining: 28d 8h 28m Buy It Now for only: $8.97 |
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 4 PDA stylus for the cross ballpoint pen $7.25 Time Remaining: 12d 15h 36m Buy It Now for only: $7.25 |
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 6 CROSS Black Broad Pt PEN BALLPOINT REFILLS Genuine $11.97 Time Remaining: 15d 12h 51m Buy It Now for only: $11.97 |
 AT Cross Company Refill for Cross Selectip Porous Point Pens Medium Point $10.07 Time Remaining: 23d 11h 30m Buy It Now for only: $10.07 |
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 2 CROSS BALL POINT REFILLS RED SOFTROLLER MED BY MONTEVERDE $5.50 Time Remaining: 18d 13h 19m Buy It Now for only: $5.50 |
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 6 GENUINE CROSS BALLPOINT REFILLS BLUE MEDIUM POINT NEW IN PACKS 3 PACKS $9.95 Time Remaining: 3d 20h 33m |
 8 CROSS Blue Fine PEN BALLPOINT REFILLS Genuine $13.37 Time Remaining: 8d 13h 54m Buy It Now for only: $13.37 |
 AT Cross Company Refill for Cross Selectip Gel Roller Ball Pens Medium $10.36 Time Remaining: 23d 11h 30m Buy It Now for only: $10.36 |
 12 Penatia Cross Black Medium SelecTip Roller Refills $7.99 Time Remaining: 21d 13h 12m Buy It Now for only: $7.99 |
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 10 PDA stylus refill for the cross ballpoint pen $12.99 Time Remaining: 16d 18h 10m Buy It Now for only: $12.99 |
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 AT Cross Company Refills for Cross Ballpoint Pens Medium Point Blue Ink $11.19 Time Remaining: 23d 11h 30m Buy It Now for only: $11.19 |
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 AT Cross Company Refills for Cross Ballpoint Pens Fine Point Blue Ink $11.19 Time Remaining: 23d 11h 30m Buy It Now for only: $11.19 |
 NEW Cross Selectip Rollerball Refill 8523 $3.99 Time Remaining: 22d 15h 7m Buy It Now for only: $3.99 |
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 ONE LOT OF CROSS REFILLS 8405 FOR 5MM LEAD PENCILS WITH ERASURE $9.99 Time Remaining: 5d 17h 46m |
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Refills Cross
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What will the rate be?
Please help!
A child loves to watch as you refill a transparent plastic bottle with shampoo. Every horizontal cross-section is a circle, but the diameters of the circles have different values, because the bottle is much wider in some places than in others. You pour in bright green shampoo with constant volume flow rate 15.5 cm3/s.
(a) At what rate is the level of the shampoo in the bottle rising at a point where the diameter of the bottle is 6.50 cm?
(b) At what rate is the level of the shampoo rising at a point where the diameter is 1.25 cm?
I have no idea how to approach this problem
The volume cross-sections are cylinders with infinitestimal height:
dV = πr² dh
dV/dt = π(D/2)² (dh/dt)
(a)
15.5 cm³/s = π(6.50 cm / 2)² (dh/dt)
dh/dt = 0.467 cm/s
(b)
15.5 cm³/s = π(1.25 cm / 2)² (dh/dt)
dh/dt = 12.6 cm/s
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