Respuesta :
the volume of water in the pool is 3600 cubic feet.
Let's break the pool up into 10-foot squares and use the midpoint rule.
T he 20' dimension has 2 squares --> m = 2 --> Δx = [tex]\frac{20}{2}[/tex] = 10
The 30' dimension has 3 squares --> n = 3 --> Δy =  [tex]\frac{30}{3}[/tex]= 10
The corners and midpoints of each square will be:
(0,0) ... (10,0) ... (20,0) ... (30,0)
.... (5, 5) ... (15,5) ... (25, 5)
(0,10). (10,10). (20,10). (30,10)
..... (5,15) .. (15,15). (25, 15)
(0,20). (10,20). (20,20). (30,20)
Therefore, the midpoint rule yields an approximate volume
Δx Δy * Σ f(x*,y*), where (x*,y*) are the above 6 midpoint points
= 10 * 10 [f(5,5) + f(15,5) + f(25,5) + f(5,15) + f(15,15) + f(25,15)]
= 100 [3 + 7 + 10 + 3 + 5 + 8]
= 100(36)
= 3600 cubic feet
Extent is a degree of occupied three-dimensional space. it's far often quantified numerically through the usage of SI-derived devices (consisting of the cubic meter and liter) or by way of numerous imperial or US standard units (along with the gallon, quart, and cubic inch). The definition of the period (cubed) is interrelated with the extent. The volume of a container is generally understood to be the ability of the container; i.e., the quantity of fluid (gasoline or liquid) that the field could preserve, in place of the amount of space the field itself displaces.
In historic times, volume is measured using comparable-formed natural bins and afterward, standardized packing containers. a few easy 3-dimensional shapes will have their extent effortlessly calculated using mathematics formulas. Volumes of more complex shapes may be calculated with imperative calculus if a formula exists for the shape's boundary. 0-, one- and -dimensional items don't have any volume; in fourth and better dimensions, a similar idea to the ordinary volume is the hypervolume.
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