AP Calculus Related Rates Formulas Flashcards
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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) (D)</p> Signup and view all the answers

What is the formula for the Area of a Square?

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

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

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

What is the formula for the Perimeter of a Rectangle?

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

What is the formula for the Volume of a Cone?

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

What is the formula for the Volume of a Cube?

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

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

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

What is the equation of a Circle?

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

What is the formula for the Circumference of a Circle?

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

What is the formula for the Volume of a Sphere?

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

What is the alternative form of the Pythagorean Theorem?

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

What is the formula for the Perimeter of a Square?

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

What is the formula for the Area of a Rectangle?

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

What is the formula for the Area of a Triangle?

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

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

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

Flashcards

Area of a Circle

The area inside a circle is calculated using pi (π) multiplied by the radius (r) squared.

Volume of a Cylinder

Volume of a cylinder is the amount of space it occupies, found by pi (π) times the radius (r) squared times height (h).

Pythagorean Theorem

In a right-angled triangle, the square of the hypotenuse (side opposite the right angle) is equal to the sum of the squares of the other two sides.

Surface Area of a Cylinder

The total area of the curved surface and both circular ends of a cylinder.

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Area of a Square

Side Length (s) times Side Length (s) or squared the side.

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Surface Area of a Sphere

Total area of the sphere's surface.

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Perimeter of a Rectangle

The total distance around the rectangle.

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Volume of a Cone

Amount of space a cone contains.

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Volume of a Cube

Space a cube occupies.

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Surface Area of a Cube

Total surface area of a cube.

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Equation of a Circle

Standard equation defining a circle.

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Circumference of a Circle

Distance around a circle.

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Volume of a Sphere

Space occupied by a sphere.

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Perimeter of a Square

The total distance around the square.

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Area of a Rectangle

Area inside a rectangle.

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Area of a Triangle

Area inside a triangle.

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Area of an Equilateral Triangle

Area of a triangle with all sides equal.

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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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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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