💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

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, 79, 94, 106, 117, 128, 63, 39, and 0. Use the Midpoint Rule to estimate the volume of the liver.

1110 $\mathrm{cm}^{3}$

02:03

Wen Z.

00:41

Amrita B.

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 2

Volumes

Oregon State University

Baylor University

Idaho State University

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:58

A CAT scan produces equall…

03:44

A cross-section of an airp…

01:31

Suppose an MRI scan indica…

01:50

11:56

Cerebral blood flow The ta…

01:08

Estimate the volume from t…

01:51

This cat (or cats?) is wal…

06:37

07:52

Volume of a wooden object …

Alright, so I've taken the liberty of doing two things here, I've written down all of the values that we have for the cross sectional areas. We're here on the left side. And I have also written out there mid points here in the second column. Um and remember that to find the midpoint, we just add we just take the average of these two values. zero was 18 over to equals nine and 18 58/2 years, 30 years and we did that for all of these. Um it's rather time consuming, but this is going to be the result. Um After that, what midpoint rule tells us Is that in order to approximately the volume here we're going to need to uh take 1.5 which is the distance between the cross sections. And we multiply 1.5 x nine, Which is one minute point, then add to that 1.5 times 30 years. Then add to that 1.5 times 68.5 et cetera. And we can also uh do something somewhat simpler, which is first we add all of these midpoint values and then we multiply by 1.5 we just distribute us uh The 1.5. So um uh if you add up all these mid points you can do this by hand. I wouldn't recommend it, I just do a calculator but if you add all these up you are going to get 900 Which is pretty useful because that means that multiplying by 1.5 is very easy. 1.5 times 900 is just going to be 1350. So we're going to get uh, 1350. Now, of course, we need units for this. Can't just save 13.50. So we recall the units that we had, um, the areas were measured in square centimeters and then 1.5 was the distance between the cross sections in centimeters. So our units are just going to be cubic centimeters because we have spare centimeters multiplied by regular centimeters. So we have 13 50. Keep accelerators. That is going to be our approximation for the volume. Hey,

Numerade Educator

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

A CAT scan produces equally spaced cross-sectional viewsof a human organ…

A cross-section of an airplane wing is shown. Measurements of the thickness …

Suppose an MRI scan indicates that cross-sectional areas of adjacent slices …

Cerebral blood flow The table shows measurements of $A(t),$ the concentratio…

Estimate the volume from the cross-sectional areas.$$\begin{array}{|l|l|…

This cat (or cats?) is walking through a 25 cylindrical pipe.(FIGURE CA…

Volume of a wooden object A solid wooden object turned on a lathe has a leng…

Estimate the volume from the cross-sectional areas.$$\begin{array}{|l|c|…