   # Glacier Horizontal cross sections of a piece of ice that broke from a glacier are in the shape of a quarter of a circle with a radius of approximately 50 feet. The base is divided into 20 subregions, as shown in the figure. At the center of each sub region, the height of the ice is measured, yielding the following points in cylindrical coordinates. ( 5 , π 1 6 , 7 ) , ( 15 , π 1 6 , 8 ) , ( 25 , π 1 6 , 10 ) , ( 35 , π 1 6 , 12 ) , ( 45 , π 1 6 , 9 ) ( 5 , π 1 6 , 9 ) , ( 15 , π 1 6 , 10 ) , ( 25 , 3 π 1 6 , 14 ) , ( 35 , 3 π 1 6 , 15 ) , ( 45 , 3 π 1 6 , 10 ) ( 5 , 5 π 1 6 , 9 ) , ( 15 , 5 π 1 6 , 11 ) , ( 25 , 5 π 1 6 , 15 ) , ( 35 , 5 π 1 6 , 18 ) , ( 45 , 5 π 1 6 , 14 ) ( 5 , 7 π 1 6 , 5 ) , ( 15 , 7 π 1 6 , 8 ) , ( 25 , 7 π 1 6 , 11 ) , ( 35 , 7 π 1 6 , 16 ) , ( 45 , 7 π 1 6 , 12 ) (a) Approximate the volume of the piece of ice. (b) Ice weighs approximately 57 pounds per cubic foot. Approximate the weight of the piece of ice. (c) There are 7.48 gallons of water per cubic foot. Approximate the number of gallons of water in the piece ### Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378

#### Solutions

Chapter
Section ### Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378
Chapter 14.3, Problem 58E
Textbook Problem
1 views

## GlacierHorizontal cross sections of a piece of ice that broke from a glacier are in the shape of a quarter of a circle with a radius of approximately 50 feet. The base is divided into 20 subregions, as shown in the figure. At the center of each sub region, the height of the ice is measured, yielding the following points in cylindrical coordinates. ( 5 , π 1 6 , 7 ) , ( 15 , π 1 6 , 8 ) , ( 25 , π 1 6 , 10 ) , ( 35 , π 1 6 , 12 ) , ( 45 , π 1 6 , 9 ) ( 5 , π 1 6 , 9 ) , ( 15 , π 1 6 , 10 ) , ( 25 , 3 π 1 6 , 14 ) , ( 35 , 3 π 1 6 , 15 ) , ( 45 , 3 π 1 6 , 10 ) ( 5 , 5 π 1 6 , 9 ) , ( 15 , 5 π 1 6 , 11 ) , ( 25 , 5 π 1 6 , 15 ) , ( 35 , 5 π 1 6 , 18 ) , ( 45 , 5 π 1 6 , 14 ) ( 5 , 7 π 1 6 , 5 ) , ( 15 , 7 π 1 6 , 8 ) , ( 25 , 7 π 1 6 , 11 ) , ( 35 , 7 π 1 6 , 16 ) , ( 45 , 7 π 1 6 , 12 ) (a) Approximate the volume of the piece of ice.(b) Ice weighs approximately 57 pounds per cubic foot. Approximate the weight of the piece of ice.(c) There are 7.48 gallons of water per cubic foot. Approximate the number of gallons of water in the piece (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

### Explanation of Solution

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,π16,7),(15,π16,8),(25,π16,10),(35,π16,12),(45,π16,9)(5,3π16,9),(15,3π16,10),(25,3π16,14),(35,3π16,15),(45,3π16,10)(5,5π16,9),(15,5π16,11),(25,5π16,15),(35,5π16,18),(45,5π16,14)(5,7π16,5),(15,7π16,8),(25,7π16,11),(35,7π16,16),(45,7π16,12)

And,

Calculation:

It is known that the volume of the sub-region which is determined by points (5,π16,7) is:

base×height=(5×10×π8)×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×π8)×7+(5×10×π8)×9+(5×10×π8)×9+(5×10×π8)×5+(15×10×π8)×8+(15×10×π8)×10+(15×10×π8)×11+(15×10×π8)×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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