Solving Geometric Shapes

Introduction

                   The geometrical shapes are point, line, square, rectangle, and circle. The point is used to specify a location. The line extends infinitely in both directions. The square has the same length on each side. The rectangle has the opposite sides are equal. The other Geometrical shapes are like circle, triangle. In the line segment part of a line between two points are called end point.

 

Formula for basic geometric shapes:

 

            Generally the geometric shapes classified into flat geometric shapes and solid geometric shapes. The flat geometric shapes are like square, rectangle, circle, etc. The solid geometric shapes are like cone, cube, sphere, and cylinder, etc.    

Square     : Area = a2

                  Perimeter = 4a

Rectangle: Area = l w

                  Perimeter = 2(l + w)

Triangle    :Area = ( ½) bh

                  Perimeter = a + b + c

Circle        :Area =` pi` r2                              ` pi` = 3.14(constant)

                  Perimeter = 2` pi`

Volume    : Sphere =` 4/3` ` pi` r3

                  Cylinder = ` pi` r2 h

                  Cone =`1/3` ` pi` r2 h

                  Cube = a3

 

Solved problems:

 

Solving Geometric problem 1: Find the volume of the sphere whose diameter is 42 inches.

  Sol :            Volume of sphere = `4/3 ` ` pi` r3

                         Diameter = 42 inches

                             Radius = diameter / 2

                                        = 42 / 2

                                        = 21 inches

                           Volume =  `4/3` ` pi` r3

                                       = ` 4/3` × 3.14 ×21×21×21

                                       = 4.187×21×21×21

                                       = 38776 cubic inches (approximately)


Solving Geometric problem 2: Find the volume of the cylindrical canister with radius   5 cm and height 8 cm.

   Sol :              Volume of cylinder = ` pi` r2 h

                           Radius (r) = 5 cm

                           Height (h) = 8 cm

                              Volume = 3.14 × 5 × 5 × 8

                                          = 628 cm3


Solving Geometric problem 3:  What is the area and perimeter of a square that has a side of 8m?

    Sol :           Side (a)   = 8 m

                        Area = a2

                                = 8 × 8

                                =   64 m2

                 Perimeter = 4a

                                 = 4 × 8

                                 = 32m

Solving Geometric problem 4:  Find the area of triangle .the height of the triangle is 10m and base 3m.

      Sol :       Height (h) = 10 cm

                      Base (b) = 3cm

                         Area = bh

                                 = `1/2` × 3 × 10

                                 = 15cm2

Solving Geometric problem 5:  Find the area and perimeter of rectangle length 15m and width 5m

   Sol :       Length l = 15m

                  Width (w) = 5m

                          Area = lw

                                  = 15 × 5

                                  = 75 m2

                   Perimeter = 2( l+w)

                                  = 2(15 + 5)

                                  = 2 × 20

                                  = 40m

 

I am planning to write more post on Geometry Definition with example, Foci of an Ellipse. Keep checking my blog.


Practice problem for solving geometric shapes:

Geometric problem:  What is the Perimeter of a circle having a radius of 4 cm?

       Ans:

                 Perimeter = 25.12 cm