Explanation Given information: A hemispherical bowl with radius 10 ft is filled with water to a level of 6 ft. Formula used: The work done is measured by W = F d , where F is the force applied on an object and d is the distance it travelled through. Calculation: W = F d Set up the coordinate system with the origin at the vertex of the circle. The centre and radius of the circle is ( 0 , 10 ) and 10 ft, therefore, its equation is r 2 + ( y − 10 ) 2 = 10 2 r = 100 − ( y − 10 ) 2 F = A r e a × d e n s i t y = π r 2 × 62.4 = π [ 100 − ( y − 10 ) 2 ] 2 × 62.4 = π [ 100 − ( y − 10 ) 2 ] × 62.4 = π [ 100 − ( y 2 − 20 y + 100 ) ] × 62.4 = 62.4 π [ 20 y − y 2 ] The slab of the water must be pumped ( 10 − y ) feet, therefore the distance is ( 10 − y ) feet

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 6.5, Problem 39PS

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To find:The work done is performed in pumping all the water to the top of the bowl.

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The work done is performed in pumping all the water to the top of the bowl.

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