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, 77, 95, 107, 117, 128, 62, 38, and 0. Use the Midpoint Rule with n = 5 to estimate the volume V of the liver.
V= cm^3
The given values span a distance of 10*1.5 cm = 15 cm. Dividing
this into 5 intervals of equal width, we find that each interval is
(15 cm)/5 = 3 cm wide. The midpoints will be odd multiples of 1.5
cm, corresponding to given values. The volume can be estimated
as
.. volume = (3 cm)(18 cm^2) + (3 cm)(77 cm^2) + (3 cm)(107 cm^2) +
(3 cm)(128 cm^2) + (3 cm)(38 cm^2)
.. = (3 cm)((18 + 77 + 107 + 128 + 38) cm^2)
.. = (3*368) cm^3
.. = 1104 cm^3
A CAT scan produces equally spaced cross-sectional views of a human organ that provide information about...
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, 58, 77, 94, 106, 117, 129, 63, 38, and 0. Use the Midpoint Rule with n = 5 to estimate the volume V of the liver.