Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 6 - Applications of Integration - 6.7 Physical Applications - 6.7 Exercises - Page 468: 28

Answer

a) $3940813.825 \ J$ b) Not true

Work Step by Step

a) We need to use the formula such as: $W=\int_a^b \rho g A(y) D(y) \ dy$. Plug in the above formula the given values to obtain: $W=\int \rho g A(y) D(y) \ dy\\=\int_0^{2.5} \rho g (8-y) (4 \pi) \ dy\\=4 \pi \times \rho g \times 32 \\=3940813.825 \ J$ b) The given statement is not true because there is equal amount of water at every height pumping water from the bottom of the tank that requires greater work so that it can be lifted to the greater height than the water form the top of the tank.
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