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IBMathsDPApplications & Interpretation (AI)HLFlashcards3. Geometry & TrigonometryGeometry of 3D Shapes

Geometry of 3D Shapes (DP IB Applications & Interpretation (AI))

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Cards in this collection (19)

  • What do the x and y axes typically represent in a 3D Cartesian system?

    In a 3D Cartesian system, the x and y axes typically represent lateral space (length and width).

  • What does the z-axis typically represent in a 3D Cartesian system?

    In a 3D Cartesian system, the z-axis typically represents vertical height.

  • State the expression for the midpoint of two points, open parentheses x subscript 1 comma space y subscript 1 comma space z subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 comma space z subscript 2 close parentheses in 3D.

    The expression for the midpoint of two points, open parentheses x subscript 1 comma space y subscript 1 comma space z subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 comma space z subscript 2 close parentheses in 3D is open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction comma space fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction comma space fraction numerator z subscript 1 plus z subscript 2 over denominator 2 end fraction close parentheses

    This is given in your exam formula booklet.

  • What is the formula for finding the distance between two points open parentheses x subscript 1 comma space y subscript 1 comma space z subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 comma space z subscript 2 close parentheses in 3D?

    The distance between two points is calculated using the formula, d equals square root of open parentheses x subscript 1 minus x subscript 2 close parentheses squared plus open parentheses y subscript 1 minus y subscript 2 close parentheses squared plus open parentheses z subscript 1 minus z subscript 2 close parentheses squared end root

    Where:

    • d is the distance between two points

    • open parentheses x subscript 1 comma space y subscript 1 comma space z subscript 1 close parentheses is the set of coordinates for a known point

    • open parentheses x subscript 2 comma space y subscript 2 comma space z subscript 2 close parentheses is the set of coordinates for another known point

    This is given in your exam formula booklet.

  • Define the term prism.

    A prism is a 3D shape with a constant cross-section.

    It has two identical base shapes connected by parallel edges.

  • State the formula for the volume of a prism.

    The formula for the volume of a prism is V equals A h

    Where:

    • V is the volume of the prism

    • A is the area of the cross-section

    • h is the height of the prism

    This is given in your exam formula booklet.

  • What is the formula for the volume of a cuboid?

    The formula for the volume of a cuboid is V equals l w h

    Where:

    • V is the volume of the cuboid

    • l is the length of the cuboid

    • w is the width of the cuboid

    • h is the height of the cuboid

    This is given in your exam formula booklet.

  • What is the formula for the volume of a cylinder?

    The formula for the volume of a cylinder is V equals pi r squared h

    Where:

    • V is the volume of the cylinder

    • r is the radius of the circular base of the cylinder

    • h is the height of the cylinder

    This is given in your exam formula booklet.

  • Define the term right pyramid.

    A right pyramid is a pyramid where the apex is vertically above the centre of the base.

  • Define the term right cone.

    A right cone is a cone where the apex is vertically above the centre of the base.

  • True or False?

    The slant height of a cone is the same as its vertical height.

    False.

    The slant height of a cone is not the same as its vertical height.

    The slant height, l, of a cone is the hypotenuse of the right triangle formed by the radius, vertical height and slant height of the cone.

  • What is the formula for the volume of a right cone?

    The formula for the volume of a right cone is V equals 1 third pi r squared h

    Where:

    • V is the volume of the cone

    • r is the radius of the circular base of the cone

    • h is the vertical (perpendicular) height of the cone

    This is given in your exam formula booklet.

  • What is the formula for the volume of a right pyramid?

    The formula for the volume of a right pyramid is V equals 1 third A h

    Where:

    • V is the volume of the pyramid

    • A is the area of the base of the pyramid

    • h is the vertical (perpendicular) height of the pyramid

    This is given in your exam formula booklet.

  • What is the formula for the volume of a sphere?

    The formula for the volume of a sphere is V equals 4 over 3 pi r cubed

    Where:

    • V is the volume of the sphere

    • r is the radius of the sphere

    This is given in your exam formula booklet.

  • What is the formula for the curved surface area of a cylinder?

    The formula for the curved surface area of a cylinder is A equals 2 pi r h

    Where:

    • A is the curved surface area of the cylinder

    • r is the radius of the cylinder

    • h is the height of the cylinder

    This is given in your exam formula booklet.

  • How is the formula for the total surface area of a cylinder different to the formula for the curved surface area?

    The formula for the total surface area of a cylinder is different to the formula for the curved surface area as it includes the two end circular faces.

  • State the formula for the total surface area of a cone.

    The formula for the total surface area of a cone is A equals pi r squared plus pi r l

    Where:

    • A is the total surface area of the cone

    • r is the radius of the circular base of the cone

    • l is the slant height of the cone

    This is not given in the exam formula booklet, however the curved surface area of a cone (pi r l) and the area of a circle (pi r squared) are.

  • What is the formula for the surface area of a sphere?

    The formula for the surface area of a sphere is A equals 4 pi r squared

    Where:

    • A is the surface area of the sphere

    • r is the radius of the sphere

    This is given in your exam formula booklet.

  • True or False?

    The surface area of prisms and pyramids with polygon bases is found by adding up the areas of flat faces only.

    True.

    The surface area of prisms and pyramids with polygon bases is found by adding up the areas of flat faces only.

Previous:Geometry ToolkitNext:Trigonometry

    1. Topic 1

      Number Toolkit

    2. Topic 2

      Exponentials & Logs

    3. Topic 3

      Sequences & Series

    4. Topic 4

      Financial Applications

    5. Topic 5

      Complex Numbers

    6. Topic 6

      Further Complex Numbers

    7. Topic 7

      Matrices

    8. Topic 8

      Eigenvalues & Eigenvectors

    1. Topic 1

      Linear Functions & Graphs

    2. Topic 2

      Further Functions & Graphs

    3. Topic 3

      Modelling with Functions

    4. Topic 4

      Functions Toolkit

    5. Topic 5

      Transformations of Graphs

    6. Topic 6

      Modelling with Logarithmic, Logistic & Piecewise Functions

    1. Topic 1

      Geometry Toolkit

    2. Topic 2

      Geometry of 3D Shapes

    3. Topic 3

      Trigonometry

    4. Topic 4

      Trigonometric Identities & Equations

    5. Topic 5

      Voronoi Diagrams

    6. Topic 6

      Matrix Transformations

    7. Topic 7

      Vector Properties

    8. Topic 8

      Vector Equations of Lines

    9. Topic 9

      Modelling with Vectors

    10. Topic 10

      Graph Theory

    1. Topic 1

      Statistics Toolkit

    2. Topic 2

      Correlation & Regression

    3. Topic 3

      Non-linear Regression

    4. Topic 4

      Probability

    5. Topic 5

      Probability Distributions

    6. Topic 6

      Random Variables

    7. Topic 7

      Binomial Distribution

    8. Topic 8

      Normal Distribution

    9. Topic 9

      Combinations of Normal Distributions & Sample Mean Distributions

    10. Topic 10

      Poisson Distribution

    11. Topic 11

      Hypothesis Testing using the Chi-squared Distribution

    12. Topic 12

      Hypothesis Testing for Population Parameters

    13. Topic 13

      Transition Matrices & Markov Chains

    1. Topic 1

      Differentiation

    2. Topic 2

      Further Differentiation

    3. Topic 3

      Integration

    4. Topic 4

      Further Integration

    5. Topic 5

      Kinematics

    6. Topic 6

      Differential Equations

    7. Topic 7

      Coupled & Second Order Differential Equations