Through some crude and approximate measurement techniques. such as pacing, it is

Question

Through some crude and approximate measurement techniques. such as pacing, it is determined that a swimming pool is 20 ft. Wide, 40 ft. Long, and 6 ft. Deep. The width and length measurements are accurate to the nearest foot. The depth measurement is accurate to the nearest 0.5 ft. Required: A. Determine your best estimate of the volume of the swimming pool (cubic feet) B. Determine the range of the possible volumes of the swimming pool. C. If it was desired to determine the volume of the swimming pool to within 1 cubic fool, approximately what accuracy would be needed in the individual measurements of the width, length, and depth. Assume that all measurements will be made to the same accuracy (for example, to the nearest one-quarter foot).

Explanation / Answer

dimensions=20ftx40ftx6ft

a)Best Estimate=20*40*6=4800cubic feet

b)As width and length are accurate to nearest foot meaning

width->(19.5,20.5) and length->(39.5,40.5)

As depth is accurate to nearest 0.5f->Depth->(5.75,6.25)

Max possible=20.5*40.5*6.25=5189.063

Min possible=19.5*39.5*5.75=4428.938

Range->(4428.938,5189.063) cubic feet

C)Let the accuracy by 2x

Hence Range->[(20-x)(40-x)(6-x),(20+x)(40+x)(6+x)]

Range=1cubic foot

Hence difference =1cubic foot

(20+x)(40+x)(6+x)-(20-x)(40-x)(6-x)=1. Solving for x gives x=0.000431

Hence accuracy should be within 2x=0.00086ft

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