Acat scan of a human pancreas shows cross-sections spaced 1 cm apart. the pancreas is 12 cm long and the cross-sectional areas, in square centimeters, are 0, 7.9, 15.3, 18.1, 10.2, 10.7, 9.5, 8.5, 7.8, 5.6, 4.2, 2.7, and 0. use the midpoint rule to estimate the volume of the pancreas.

100.5 cubic centimeters.

Step-by-step explanation:

The 12 intervals of the scanning are the 1-cm width intervals

[0,1), [1,2), [2,3), [3,4), [4,5), [5,6), [6,7), [7,8), [8,9), [9,10), [10,11), [11,12] and their midpoints are

0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5, 10.5 and 11.5

The idea here is to the volume of the pancreas by approximating it with the volume V of 12 cylinders of height h=1 and area of the base A equals to the area given for the scanning where that midpoints fall.

Since the volume of a cylinder equals area of the base times height and all the cylinders have the same height of 1 cm, the sum of the volumes of the 12 cylinders equals the sum of the areas of the cross-sections multiplied by 1 cm (so the result is given in cubic centimeters)

Estimation of the volume of the pancreas

7.9+15.3+18.1+10.2+10.7+9.5+8.5+7.8+5.6+4.2+2.7 cubic cm

=100.5 c.c.

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