A vacant, cleared plot of land is rectangular with dimensions $120$ m by $85$ m

and is thought to contain a circular pollutant hot$-$spot of $25$ m diameter but

there is no information on where it might be located within the site. Test

bores are to be drilled for soil and groundwater samples. Using Ferguson$$s

recommendations, devise an economical sampling scheme which minimises

the number of test bores but gives a $95\%$ probability of detecting the hot$-$spot.

Calculate the minimum number of sample points required. Suggest a practical

distribution and the number of sample positions along length and breadth of

the site and their spacings, which may be more than the minimum, but provide

optimal coverage of the plot with similar spacings in the perpendicular

horizontal directions.

Answer: Minimum Number of Samples $=$

Answer: Number of samples along the length axis $=,$ spacing $($m$)$

Answer: Number of samples along the breadth axis $=,$ spacing $($m$)$