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AP Calculus Related Rates Formulas Flashcards
18 Questions
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AP Calculus Related Rates Formulas Flashcards

Created by
@BeneficentHonor6192

Questions and Answers

What is the formula for the Area of a Circle?

  • A = 4πr^2
  • A = 2πr
  • A = πr^2 (correct)
  • A = πd^2

    • What is the formula for the Volume of a Cylinder?

  • V = 2πrh
  • V = πrh^2
  • V = π(r^2)h (correct)
  • V = (⅓)π(r^2)h

    • What is the Pythagorean Theorem?

  • (A^2) + (B^2) = 2C
  • (A^2) + (B^2) = (C^2) (correct)
  • (C^2) - (A^2) = (B^2)
  • (A + B)^2 = C^2

    • What is the formula for the Surface Area of a Cylinder?

    <p>S = 2πrh + 2π(r^2)</p> Signup and view all the answers

    What is the formula for the Area of a Square?

    <p>A = s^2</p> Signup and view all the answers

    What is the formula for the Surface Area of a Sphere?

    <p>S = 4π(r^2)</p> Signup and view all the answers

    What is the formula for the Perimeter of a Rectangle?

    <p>P = 2l + 2w</p> Signup and view all the answers

    What is the formula for the Volume of a Cone?

    <p>V = (⅓)π(r^2)h</p> Signup and view all the answers

    What is the formula for the Volume of a Cube?

    <p>V = s^3</p> Signup and view all the answers

    What is the formula for the Surface Area of a Cube?

    <p>S = 6(s^2)</p> Signup and view all the answers

    What is the equation of a Circle?

    <p>X^2 + Y^2 = R^2</p> Signup and view all the answers

    What is the formula for the Circumference of a Circle?

    <p>C = 2πr</p> Signup and view all the answers

    What is the formula for the Volume of a Sphere?

    <p>V = (4/3)π(r^3)</p> Signup and view all the answers

    What is the alternative form of the Pythagorean Theorem?

    <p>L^2 + 6^2 = h^2</p> Signup and view all the answers

    What is the formula for the Perimeter of a Square?

    <p>P = 4s</p> Signup and view all the answers

    What is the formula for the Area of a Rectangle?

    <p>A = lw</p> Signup and view all the answers

    What is the formula for the Area of a Triangle?

    <p>A = (1/2)bh</p> Signup and view all the answers

    What is the formula for the Area of an Equilateral Triangle?

    <p>A = (s^2√(3))/4</p> Signup and view all the answers

    Study Notes

    Formulas for Area and Volume

    • Area of a Circle: ( A = \pi r^2 )
    • Volume of a Cylinder: ( V = \pi (r^2)h )
    • Volume of a Cone: ( V = \frac{1}{3} \pi (r^2)h )
    • Volume of a Cube: ( V = s^3 )
    • Volume of a Sphere: ( V = \frac{4}{3} \pi (r^3) )

    Geometric Properties

    • Pythagorean Theorem: ( A^2 + B^2 = C^2 )
    • Equation of a Circle: ( X^2 + Y^2 = R^2 )
    • Area of a Square: ( A = s^2 )
    • Area of a Rectangle: ( A = lw )
    • Area of a Triangle: ( A = \frac{1}{2}bh )
    • Area of an Equilateral Triangle: ( A = \frac{s^2 \sqrt{3}}{4} )

    Surface Areas and Circumferences

    • Surface Area of a Cylinder: ( S = 2\pi rh + 2\pi(r^2) )
    • Surface Area of a Sphere: ( S = 6(s^2) ) (This is incorrect; the correct formula is ( S = 4\pi(r^2) ))
    • Circumference of a Circle: ( C = 2\pi r )

    Perimeters

    • Perimeter of a Rectangle: ( P = 2l + 2w )
    • Perimeter of a Square: ( P = 4s )

    Alternative Forms

    • Alternative Pythagorean Theorem: ( L^2 + 6^2 = h^2 )

    These formulas and definitions serve as fundamental tools for solving problems related to area, volume, and geometric properties in calculus and geometry.

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    Description

    Test your knowledge of essential formulas related to area, volume, and surface area in this AP Calculus flashcard quiz. Each flashcard presents a formula along with its definition, helping you grasp the concepts needed for related rates problems. Perfect for quick revision before your exams!

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