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Formulas: measures and solids, grade 6

The circle and the disc

  • The diameter d\displaystyle d is two radii r\displaystyle r
    d\displaystyle d =\displaystyle = 2×r\displaystyle 2\times r
  • The number pi – the value to calculate with
    π≈3.14\displaystyle \pi\approx3.14
  • The circumference of a circle – d\displaystyle d the diameter
    C\displaystyle C =\displaystyle = πd\displaystyle \pi d
  • The circumference of a circle – r\displaystyle r the radius
    C\displaystyle C =\displaystyle = 2πr\displaystyle 2\pi r
  • The area of a disc – r\displaystyle r the radius
    A\displaystyle A =\displaystyle = πr2\displaystyle \pi r^2

Volumes

  • The volume of a box – a\displaystyle a the length, b\displaystyle b the width, c\displaystyle c the height
    V\displaystyle V =\displaystyle = a×b×c\displaystyle a\times b\times c
  • The volume of a box, a prism or a cylinder – S\displaystyle S the area of the base, h\displaystyle h the height
    V\displaystyle V =\displaystyle = S×h\displaystyle S\times h
  • The volume of a cylinder – r\displaystyle r the radius of the base, h\displaystyle h the height
    V\displaystyle V =\displaystyle = πr2h\displaystyle \pi r^2 h
  • The volume of a pyramid – a third of the prism with the same base and height
    V\displaystyle V =\displaystyle = S×h3\displaystyle \frac{S\times h}{3}
  • The volume of a cone – a third of the cylinder with the same base and height
    V\displaystyle V =\displaystyle = πr2h3\displaystyle \frac{\pi r^2 h}{3}
  • The volume of a sphere – two thirds of the cylinder around it
    V\displaystyle V =\displaystyle = 23×πr2×2r\displaystyle \frac{2}{3}\times\pi r^2\times2r