Slicing the watermelon

Rating:

- (3)
- (0)
- (0)
- (0)
- (0)

Description:

To demonstrate techniques for approximating and calculating the volume of a simple ellipsoid.

This packet consists of four videos that begin with visualizing the problem geometrically, through approximating the problem and ending with setting up (but not finishing off) the calculus computation for exact volume.

(more)

Try a College Course Free

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to over 2,000 colleges and universities.*

Begin Free Trial

No credit card required

28 Sophia partners guarantee credit transfer.

253 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 21 of Sophia’s online courses. More than 2,000 colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.

Tutorial

Introduction

A common problem in Calculus I involves finding the volume of ellipsoid with circular cross-sections in one direction and elliptical cross-sections in another. The easiest physical model for this geometric object is a watermelon.

So let's find the volume of a watermelon that is 28 inches long and 25 inches in diameter. It's a big watermelon.

This packet will set up the problem twice-once as an approximation, the other using precise calculus techniques.

Visualizing the watermelon

This video helps us to visualize the watermelon and the impending slicing process.

open player in a new window

Setting up the techniques

This video sets up the paper-and-pencil techniques that are to come and focuses our attention on the important question in each case: "How does the radius of our slice change as we move further towards the end of the watermelon?"

open player in a new window