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Chapter 6: Q. 45 (page 556)

Find each mass described in Exercises 41鈥�48.

The mass of a 10-centimeter rod with square cross section of side length 1 centimeter, made of a combination of metals in such a way that the density of the rod x centimeters from the left end is 蚁(x)=15鈭�0.5xgrams per cubic centimeter.

Short Answer

Expert verified

The mass of the rod is 125 grams

Step by step solution

01

Given Information 

The mass of a 10-centimeter rod with square cross section of side length 1 centimeter, with the density of the rod x centimeters is

蚁(x)=15鈭�0.5x

02

Fromula 

Volume of cuboid = length time width times height

The length and height of cuboid is 1 inches and width is 鈭�x

Volume=lbhV=(1)(1)鈭�xV=鈭�x

03

Density 

Let xi represents slice of the rod at some point

The density throughout enter slice is

蚁(xi)=15鈭�0.5xi蚁=MV15鈭�0.5xi=M鈭�xM=鈭�x15鈭�0.5xi

04

Integration 

The approximate of the entire rod is the sum

鈭�鈭�x15鈭�0.5xi

Accumulate the mass from x= 0 to 10 to find total mass

鈭�01015鈭�0.5xdx=15x-0.5x22010=15(10)-0.5(10)22=125grams

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