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Home › Courses › Calculus 1/AB/BC › Archive for Chapter 7 – Area, Volume, and Arc Length
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Chapter 7 – Area, Volume, and Arc Length

This Chapter starts with a master class in how to find the area of a bounded region and the area between two curves.  Next, you will make simple work of how to set up and solve integrals to find the volume of solids of revolution using the Disk and Washer methods.  From there you will see the beauty of simple geometry come alive when you master finding volumes of solids with cross-sections.  You will then rock how to find volumes of solids of revolution using the Shell Method.  After this, you will explore the concepts of arc length and surface area.  The chapter wraps up with original AB and BC free response questions that incorporate many of the above topics.  Time to see how basic geometry with a little Calculus can make for some awesome concepts!

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Lesson 1 – Area Between Two Curves

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Lesson 1 – Area Between Two Curves (Part 2)

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Lesson 2 – Volume of Solids of Revolution: Disk and Washer Methods

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Lesson 2 – Volume of Solids of Revolution: Disk and Washer Methods (Part 2)

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Lesson 2 – Volume of Solids of Revolution: Disk and Washer Methods (Part 3)

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Lesson 3 – Volumes of Solids with Known Cross-Sections

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Lesson 4 – The Shell Method

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Lesson 5 – Arc Length and Surface Area

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Lesson 6 – AB and BC Exam Practice Problems

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    June 8, 2018

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    August 10, 2017
  • positive review  Matt truly cares about each student. My son took his SAT prep course and his math section increased 90 points. There was great communication after each course session as the teachers would email what was covered, what to do next, and an overview of future class. He was always there to answer any question my son ( and I) had.

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    March 26, 2019

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    October 11, 2017
  • I took a Calc. 2 class at BCCC this semester and we missed 3 weeks of class due to snow, meaning my professor had to condence the material and breeze by a lot of important concepts. If it hadn't been for Matt there is no way I would've passed the course. He presented everything in a clear, comprehensive, and easy to understand way that I've never really experienced before and I did really well because of it. He took the time to explain everything, answered all of my questions and made sure that I was keeping up with him every step of the. He's a genuine guy who really wants you to learn and enjoys teaching. I highly recommend him for anyone who is struggling with their course work, you'll never make a better investment.

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    August 13, 2017
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    December 27, 2017

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    Amy Cimino Bodnar Avatar Amy Cimino Bodnar
    January 25, 2019
  • After class with Mr. Groden, I felt more than prepared for my exams. In class, we had covered every type of problem we could expect to see and received ample explanation of its solution. On the day of the test, I was calm knowing Mr. Groden had prepared me well for any problem that could be on the exam. In addition to giving me confidence going into one of the most difficult exams I had taken, Mr. Groden gave me a deeper appreciation and understanding of mathematics. He gave me the ability to visualize complex concepts more than any other teach I had and problem solving techniques that I continue to use. Beyond being ready for my exams, I was ready to understand more difficult math in high school and college.

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    January 16, 2017

    positive review  I had Matt Groden for AP Calculus and I have to say, he was and probably will be the greatest teacher I ever had. Not only was he exceptional in terms of his teaching ability and breadth of knowledge, but it is his care for learning was what made him unique. This was the first teacher in a long time that I can remember who valued learning and discovery over just memorizing and ‘teaching to the test’. His ability to make students excited to learn new math material is what makes Matt so perfectly suited for this. Anyone with the chance to learn math with him should most definitely take this opportunity - you will not be disappointed!!

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    March 4, 2019
  • If you are looking for an enthusiastic teacher who makes understanding math easy then look no further. Matt came to our rescue when my daughter was struggling in AP Calculus BC. Not only was he able to boost her grade to an A, she also scored a 5 on her AP exam for both Calculus AB and BC. Also, My son went to his SAT class over the summer and after every class he said how much he enjoyed Matt and was excited about what he learned. I will continue to give Matt the highest recommendation which is rare for me since I am a math teacher myself. He is excellent!

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    August 7, 2017

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    August 31, 2018
  • My daughter (who usually gets straight A's) was struggling in Pre-Calculus with a D+ current grade. After tutoring with Mr. Grodan, she got an A on her final and ended up passing the class with a B. I recommend his services to anyone who is struggling with math.

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    June 30, 2017

    Both of our sons were extremely fortunate to have Mr. Groden for AP Calculus. He is enthusiastic, clear and an all-around outstanding teacher. He motivates his students and consistently shows great interest in their well being, both in and out of the classroom. Both our sons were extremely well prepared for the AP exam. Thank you!

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    January 16, 2017
  • Matt is amazing! Both of my children see him weekly and they love when he comes to tutor. He is extremely knowledgeable and has a different perspective on teaching math the the kids really get excited about. I don't think I have met anyone more enthusiastic about math, ever. It's inspiring for the kids to work with someone that truly loves teaching math!

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    June 12, 2017

    My son took the SAT prep class. It was a great class with fantastic instruction strategies and top notch teachers who clearly know their stuff. They made the class fun and motivated my son to do the required out-of-class practice. His scores on the practice tests consistently improved. We would absolutely recommend this class!

    Andrea Evans Silverman Avatar Andrea Evans Silverman
    October 3, 2017
  • Matt has helped my son immensely in preparing both for the SATs and the AP Calculus BC exam. He has a way of explaining and teaching math that kept my son excited and energized to learn more. My son did extremely well on his SATs and was strong in Calculus, all thanks to Matt and his care for his students. If you are need for math help for your child, look no further!

    Susan Heller Steiner Avatar Susan Heller Steiner
    May 17, 2019

    positive review  Thank you for offering these summer courses. I think it is important to keep up the skills over the summer and not get summer brain. You also have a wonderful teaching style which i know my daughter appreciates.

    Toni Snedeker Scratchard Avatar Toni Snedeker Scratchard
    August 26, 2019
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      ▼
      • 6th Grade Math
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1: Whole Numbers & Decimals
        • Chapter 2: Representing Data In Different Ways
        • Chapter 3: Variables, Algebraic Expressions, & Solving Equations
        • Chapter 4: Divisibility, Factoring Numbers, & Fractions
        • Chapter 5: Addition and Subtraction of Fractions
        • Chapter 6: Multiplication and Division of Fractions
        • Chapter 7: Ratios, Proportions, and Percents
        • Chapter 8: Fundamentals of Geometry
        • Chapter 9: Unit Conversions, Perimeter, Area, & Volume
        • Chapter 10: Introduction to Probability
        • Chapter 11: Integers – Properties, Operations, & Equations
        • Chapter 12: Two-Step Equations and Inequalities
      • Pre-Algebra
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1: Algebraic Expressions & Operations with Integers
        • Chapter 2: One-Step Equations & Inequalities
        • Chapter 3: Operations and Equations With Decimals
        • Chapter 4: Factors, Simplifying Fractions, and Exponent Rules
        • Chapter 5: Fraction Operations & Solving Equations with Fractions
        • Chapter 6: Operations and Uses of Ratios, Proportions, & Percents
        • Chapter 7: Solving Equations and Inequalities
        • Chapter 8: Relations & Functions, Slope, Lines, and Graphing
        • Chapter 9: Foundations of Geometry
        • Chapter 10: Areas of Two- & Three-Dimensional Figures and Volume
        • Chapter 11: Right Triangles and An Introduction to Trigonometry
        • Chapter 12: Data Analysis: Techniques and Calculations
        • Chapter 13: Probability, Combinations, and Permutations
        • Chapter 14: Foundations of Non-Linear Functions and Polynomial Operations
      • Algebra 1
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1: Algebraic Expressions and Operations with Real Numbers
        • Chapter 2: Solving Equations – From One-Step to Multi-Step
        • Chapter 3: Ratios, Proportions, & Percents
        • Chapter 4: Solving Inequalities
        • Chapter 5: Introduction to Graphs and Functions
        • Chapter 6: Linear Functions and Graphing Lines
        • Chapter 7: Systems of Linear Equations and Linear Inequalities
        • Chapter 8: Exponent Rules & Exponential Functions
        • Chapter 9: Polynomials
        • Chapter 10: Graphing and Solving Quadratic Equations
        • Chapter 11: Introduction to Rational Expressions
        • Chapter 12: Radicals and An Introduction to Trigonometry
        • Chapter 13: Data Analysis: Techniques and Calculations
        • Chapter 14: Probability, Combinations, and Permutations
      • Calculus 1 & 2 / AB / BC
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1 – Limits
        • Chapter 2 – Derivatives
        • Chapter 3 – Uses of the Derivative
        • Chapter 4 – Integration
        • Chapter 5 – Derivatives and Integrals of Exponential Functions, Logarithms, and Inverse Trigonometry
        • Chapter 6 – Differential Equations and Exponential & Logistic Growth
        • Chapter 7 – Area, Volume, and Arc Length
        • Chapter 8 – Advanced Integration Techniques and Improper Integrals
        • Chapter 9 – Series and Tests for Convergence and Divergence
        • Chapter 10 – Taylor Polynomials and Power Series
        • Chapter 11 – The Calculus of Parametric and Polar Equations
    • Free Videos!
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