Question

A CAT scan produces equally spaced cross-sectional views of a human organ that provide information about the organ otherwise obtained only by surgery. Suppose that a CAT scan of a human liver shows cross-sections spaced 1.5 cm apart. The liver is 15 cm long and the cross-sectional areas, in square centimeters, are 0, 18, 59, 79, 95, 107, 118, 129, 64, 38, and 0. Use the Midpoint Rule with n = 5 to estimate the volume V of the liver.

Answer 1

V = 1113 cm³

Step-by-step explanation:

given,

length of liver = 15 cm

n = 5

`\Delta x = (b-a)/(n)`

`\Delta x = (15-0)/(5)`

`\Delta x =3`

The midpoints will be odd multiples of 1.5 cm, corresponding to given values.

values are shown in the tables attached below

V = Δx (A(1.5)+A(4.5)+A(7.5)+A(10.5)+A(13.5))

V = 3 x (18 +79 + 107 + 129 +38)

V = 3 x 371

V = 1113 cm³

volume of liver is equal to V = 1113 cm³