A CAT scan produces equally spaced cross-sectional views of a human organ that p

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, 19, 57, 79, 94, 106, 118, 129, 64, 39, and 0.

Use the Midpoint Rule with n = 3 to estimate the volume V of the liver.

Use Simpson's Rule to estimate the volume of the liver. Use all the data points.

Explanation / Answer

The given values span a distance of 10*1.5 cm = 15 cm. Dividing this into 3 intervals of equal width, we find that each interval is (15 cm)/3 = 5 cm wide. The midpoints will be odd multiples of 1.5 cm, corresponding to given values. The volume can be estimated as
.. volume = (5 cm)(57 cm^2) + (5 cm)(106 cm^2) + (5 cm)(64 cm^2)
.. = (5 cm)((57+106+64) cm^2)
.. = (5*227) cm^3
.. = 1135 cm^3

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.