max-volume-of-a-rectangular-box-inscribed-in-a-sphere-kristakingmath

Welcome to Clip from Spiral logo

Interactive video lesson plan for: Max volume of a rectangular box inscribed in a sphere (KristaKingMath)

Activity overview:

► My Partial Derivatives course: https://www.kristakingmath.com/partial-derivatives-course

► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course

Learn how to find the largest possible volume of a rectangular box inscribed in a sphere of radius r. Write down the equation of a sphere in standard form and then write an equation for the volume of the rectangular box. Since the equation for volume is the equation that needs to be optimized, solve the other equation for one of the variables and substitute the value into the volume equation so that the volume equation is reduced to two variables instead of three. Then take first-order partial derivatives of the volume equation, set them equal to 0, and use the resulting equations as a system of simultaneous equations to find critical points. Since we're dealing with a 3D figure in real space, ignore any critical numbers that have negative values for x or y. Plug the resulting critical point into the volume equation in two variables to find a value that represents the maximum volume of the rectangular box.

● ● ● GET EXTRA HELP ● ● ●

If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com

● ● ● CONNECT WITH KRISTA ● ● ●

Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com

FACEBOOK // https://www.facebook.com/KristaKingMath
TWITTER // https://twitter.com/KristaKingMath
INSTAGRAM // https://www.instagram.com/kristakingmath/
PINTEREST // https://www.pinterest.com/KristaKingMath/
GOOGLE+ // https://plus.google.com/+Integralcalc/
QUORA // https://www.quora.com/profile/Krista-King

Tagged under: expert,critical,sphere,volume,rectangular,maximum,partial derivatives,maximum volume rectangular box inscribed sphere radius ,inscribed,educational,radius ,largest,inscribed sphere,radius,largest ,sphere radius ,critical points,box,points,rectangular box,max,partial,calculus,Krista King,derivatives,simultaneous equations,

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

Play this activity

1. Students enter a simple code

2. You play the video

3. The students comment

4. You review and reflect

* Whiteboard required for teacher-paced activities

Share on:

Share Max volume of a rectangular box inscribed in a sphere (KristaKingMath) on Google+ Share Max volume of a rectangular box inscribed in a sphere (KristaKingMath) on Twitter Share Max volume of a rectangular box inscribed in a sphere (KristaKingMath) on Facebook Pin Max volume of a rectangular box inscribed in a sphere (KristaKingMath) Email Max volume of a rectangular box inscribed in a sphere (KristaKingMath)

Ready to see what else Spiral logo can do?

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.

Quickfire

Carry out a quickfire formative assessment to see what the whole class is thinking

Discuss

Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices

Clip

Turn any public video into a live chat with questions and quizzes

1000s of teachers use Spiral to deliver awesome, engaging activities that capture students' understanding during lessons.

Now it's your turn Sign up

Spiral Reviews by Teachers and Digital Learning Coaches

Spiral
Review of Spiral by teacher: Kathryn Laster @kklaster

Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech

Spiral
Review of Spiral by teacher: Room 220 Math Stars @3rdgradeBCE

Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.

Spiral
Review of Spiral by teacher: Miss Ord @ordmiss

Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral

Spiral
Review of Spiral by teacher: Adam J. Stryker @strykerstennis

Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks!

Spiral
Review of Spiral by teacher: Dr Ayla Göl @iladylayla

A good tool for supporting active #learning.

Spiral
Review of Spiral by teacher: Brett Erenberg @BrettErenberg

The Team Up app is unlike anything I have ever seen. You left NOTHING out! So impressed!

Get the Clip Chrome Extension & Create Video Lessons in Seconds

Add Clip to Chrome