(a) Explanation Given: Horizontal cross sections of a piece of ice that broke from a glacier are in the shape of quarter of a circle having 50 feet radius approximately. The base is divided into 20 sub regions. The height of ice is measured at the center of each sub-region, which gives the following points in cylindrical coordinates: ( 5 , π 16 , 7 ) , ( 15 , π 16 , 8 ) , ( 25 , π 16 , 10 ) , ( 35 , π 16 , 12 ) , ( 45 , π 16 , 9 ) ( 5 , 3 π 16 , 9 ) , ( 15 , 3 π 16 , 10 ) , ( 25 , 3 π 16 , 14 ) , ( 35 , 3 π 16 , 15 ) , ( 45 , 3 π 16 , 10 ) ( 5 , 5 π 16 , 9 ) , ( 15 , 5 π 16 , 11 ) , ( 25 , 5 π 16 , 15 ) , ( 35 , 5 π 16 , 18 ) , ( 45 , 5 π 16 , 14 ) ( 5 , 7 π 16 , 5 ) , ( 15 , 7 π 16 , 8 ) , ( 25 , 7 π 16 , 11 ) , ( 35 , 7 π 16 , 16 ) , ( 45 , 7 π 16 , 12 ) And, Calculation: It is known that the volume of the sub-region which is determined by points ( 5 , π 16 , 7 ) is: base × height = ( 5 × 10 × π 8 ) × 7 It is given that the total number of sub-regions is 20. The volume of all the sub-regions is added in order to find out the volume of the complete region, as: V = [ ( 5 × 10 × π 8 ) × 7 + ( 5 × 10 × π 8 ) × 9 + ( 5 × 10 × π 8 ) × 9 + ( 5 × 10 × π 8 ) × 5 + ( 15 × 10 × π 8 ) × 8 + ( 15 × 10 × π 8 ) × 10 + ( 15 × 10 × π 8 ) × 11 + ( 15 × 10 × π 8 ) × 8 (b) To determine To calculate: What the approximate weight of a piece of ice will be if the ice weighs 57 pounds per cubic foot. (c) To determine To calculate: What the approximate number of gallons of water will be in the piece of ice if there is 7.48 gallons of water per cubic foot.

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ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 14.3, Problem 58E

(a)

To determine

To calculate: The volume of a piece of ice that broke from a glacier and is in the shape of quarter of a circle having 50 feet radius approximately

(b)

To determine

To calculate: What the approximate weight of a piece of ice will be if the ice weighs 57 pounds per cubic foot.

(c)

To determine

To calculate: What the approximate number of gallons of water will be in the piece of ice if there is 7.48 gallons of water per cubic foot.

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Chapter 14.3, Problem 57E

Chapter 14.3, Problem 59E

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The volume of a piece of ice that broke from a glacier and is in the shape of quarter of a circle having 50 feet radius approximately

Solution Summary: The author calculates the volume of ice that broke from a glacier. The base is divided into 20 sub-regions.

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To calculate: The volume of a piece of ice that broke from a glacier and is in the shape of quarter of a circle having 50 feet radius approximately

To calculate: What the approximate weight of a piece of ice will be if the ice weighs 57 pounds per cubic foot.

To calculate: What the approximate number of gallons of water will be in the piece of ice if there is 7.48 gallons of water per cubic foot.

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Chapter 14 Solutions