Formulas For Geometry

Formulas & Definition for Geometry

Geometry is all about shapes and their properties.

  • Geometry can be divided into:-
    Plane Geometry is about flat shapes like lines, circles and triangles … shapes that can be drawn on a piece of paper.
    Solid Geometry is the geometry of three-dimensional space, the kind of space we live in.
  • Geometry is generally to discover patterns, find areas, volumes, lengths and angles, and better understand the world around us.

 

formula for geometry

Formulas To Solve Geometry

  1. Largest possible sphere that can be chiseled out from a cube of side “a” cm.
    Formula for geometry
    Diagonal of sphere is a, so radius= \frac{a}{2} \
    Remaining empty space in the cube = a3 \frac{π a^3}{6} \
  2. Largest possible cube that can be chiseled out from a sphere of radius “a” cm.
    formula of geometry
    Here OA= radius of the sphere. So, diameter of the sphere = 2a
    Let the side of the square = x, then the diagonal of the cube = √3x
    ⇒√3x = 2a ⇒ x = \frac{2a}{√3} \
  3. The largest square that can be inscribed in a right angled triangle ABC when one of its vertices
    coincide with the vertex of right of the triangle
    formula for geometry
    Side of square =  \frac{ab}{a+b} \ and are of the square =  (\frac{ab}{a+b})^2 \
  4. The largest square that can be inscribed in a semi circle of radius ‘r’ units
    formula for geometry
    Area of the square = \frac{3}{5} \ r^2
  5. The largest square that can be inscribed in a quadrant of radius ‘r’ cm.
    formula for geometry
    Side of the square =  \frac{r}{√2} \ , and area of the square =  \frac{r^2}{2} \
  6. The largest square that can be inscribed in a right angled triangle ABC when one of its vertices lies on the hypotenuse of the triangle
    formula for geometry
    side of square = \frac{abc}{a^2+b^2+ab} \
  7. The largest cube that can be chiseled out from a cone of height ‘h’ cm and radius of ‘r’ cm.formula for geometry
    Square side =  \frac{√2rh}{h+√2r} \
  8. Find the maximum volume of cylinder that can be made out of a cone of radius ‘r’ and height ‘h
    formula for geometry
    Maximum volume of the cylinder= π  \frac{2r}{3}^2 \   \frac{h}{3} \
 

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