Mensuration Formulas and Theorems
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Questions and Answers

What is the formula to calculate the circumference of a circle?

  • Circumference = radius × height
  • Circumference = 2 × π × radius (correct)
  • Circumference = π × diameter
  • Circumference = π × radius

    • What is the formula to calculate the surface area of a sphere?

  • Surface area = 2 × π × radius × (radius + height)
  • Surface area = π × radius^2 × height
  • Surface area = 4 × π × radius^2 (correct)
  • Surface area = (4/3) × π × radius^3

    • What is the formula to calculate the volume of a cylinder?

  • Volume = base × height
  • Volume = (4/3) × π × radius^3
  • Volume = π × radius^2 × height (correct)
  • Volume = length × width × height

    • What is the formula to calculate the area of a triangle?

    <p>Area = (base × height) / 2</p> Signup and view all the answers

    What is the formula to calculate the semi-perimeter of a triangle?

    <p>s = (a + b + c) / 2</p> Signup and view all the answers

    What is the name of the theorem which states that a^2 + b^2 = c^2 for right-angled triangles?

    <p>Pythagorean theorem</p> Signup and view all the answers

    Study Notes

    Definition and Importance

    • Mensuration is the branch of mathematics that deals with the measurement of geometric shapes, including their perimeter, area, and volume.
    • It is an essential concept in mathematics, physics, engineering, and other fields, as it helps in solving problems involving sizes and shapes of objects.

    Perimeter and Circumference

    • Perimeter: The distance around a two-dimensional shape, calculated by adding the lengths of all its sides.
    • Circumference: The distance around a circle, calculated using the formula: Circumference = 2 × π × radius.

    Area

    • Area of a rectangle: length × width
    • Area of a triangle: (base × height) / 2
    • Area of a circle: π × radius^2
    • Area of a parallelogram: base × height
    • Area of a trapezium: (sum of parallel sides) × height / 2

    Volume

    • Volume of a rectangular prism: length × width × height
    • Volume of a cylinder: π × radius^2 × height
    • Volume of a sphere: (4/3) × π × radius^3

    Surface Area

    • Surface area of a rectangular prism: 2 × (length × width + width × height + height × length)
    • Surface area of a sphere: 4 × π × radius^2
    • Surface area of a cylinder: 2 × π × radius × (radius + height)

    Formulas and Theorems

    • Pythagorean theorem: a^2 + b^2 = c^2 (for right-angled triangles)
    • Heron's formula: area of a triangle = √(s(s-a)(s-b)(s-c)) (where s is the semi-perimeter)
    • Brahmagupta's formula: area of a cyclic quadrilateral = √(s(s-a)(s-b)(s-c)(s-d)) (where s is the semi-perimeter)

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    Description

    Test your knowledge of mensuration, including perimeter, area, volume, and surface area of various shapes, as well as important formulas and theorems like Pythagorean theorem and Heron's formula.

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