Consider the volume of the region shown below, which shows a hemisphere of radius 3 mm and a slice of the hemisphere with width Dy = Ay. Dy Write a Riemann sum for the volume, using the slice shown: E 2pi81Dy Riemann sum = Now write an integral that gives this volume S 2pi*81dy where a = and b Finally, calculate the exact volume of the region, using your integral volume = 2/3pi*27 mm^3 (include units)

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter65: Achievement Review—section Six
Section: Chapter Questions
Problem 51AR
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Consider the volume of the region shown below, which shows a hemisphere of radius 3 mm and a slice of the
hemisphere with width Dy = Ay.
Dy
Write a Riemann sum for the volume, using the slice shown:
E 2pi81Dy
Riemann sum =
Now write an integral that gives this volume
S 2pi*81dy
where a =
and b
Finally, calculate the exact volume of the region, using your integral
volume = 2/3pi*27 mm^3
(include units)
Transcribed Image Text:Consider the volume of the region shown below, which shows a hemisphere of radius 3 mm and a slice of the hemisphere with width Dy = Ay. Dy Write a Riemann sum for the volume, using the slice shown: E 2pi81Dy Riemann sum = Now write an integral that gives this volume S 2pi*81dy where a = and b Finally, calculate the exact volume of the region, using your integral volume = 2/3pi*27 mm^3 (include units)
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