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: 29

Answer

$3944835.06 \ J$

Work Step by Step

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: $W=\int_a^b \rho g A(y) D(y) \ dy\\=4 \pi \int_0^{4} \rho g (10-y) \ dy\\=4 \pi \times \rho g \times [10y-\dfrac{y^2}{2}]_0^4 \\=128 \rho g \pi\\=(128) (1000) (9.81) (\pi)\\=3944835.06 \ J$
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