Geometry Solid Circle

In geometry, there are nine regular solids. In which some solids has the base in circle form. The right cone and cylinder are comes under that category. These are three dimensional shapes. Its surfaces are curved in shape. In this article we shall discuss about some geometry solids (right cone and cylinder) with example problems.

Solid geometry:

Right cone:
            It is a one type geometry shape.It has one flat surface. It is called base of the cone, which is in circle form. The shape of right cone is shown in below.

Surface area of the cone (A) = π r s + π r² square units
The volume of the cone (V) =1/3 π r² h cubic units
            S – Slant height
            r – Radius of base
            h – Height

Cylinder:
            It is a one type geometry shape.It has two flat surfaces. Both are circle form. One is called base another is called top. The shape of the cylinder is shown in figure.

            Surface area of the cylinder (A) = 2 π r² + 2 π r h square units
            The volume of the cylinder (V) = π r² h cubic unit
                        r – Radius
                        h – Height

geometry solid circle -Example problem:

1. The radius of the circle 5cm, height 12 cm and slant height 13 cm. find the surface area and volume of the cone.

Solution:
Given:
                  Radius (r) = 5cm
                  Height (h) = 12cm
                  Slant height (s) = 13 cm

Surface area of the cone (A) = π r s + π r²
                                                                  = (3.14 x 5 x 13) + (3.14 x 5²)
                                                                  = 204.1 + 78.5
                                                                  = 282.6
Surface area of the cone (A) = 282.6 cm²    
     
The volume of the cone (V) =1/3 π r² h
                                                                  = 1/3 x 3.14 x 5² x 12
                                                                  = 1/3 x 3.14 x 25 x 12
                                                                  = 314
The volume of the cone (V) = 314 cm³

1. The cylinder has the radius 6 cm and height 12 cm. find surface area and volume of the cylinder.

Solution:
Given:
                  Radius(r) = 6cm
                  Height (h) = 12 cm

 Formula:
Surface area of the cylinder (A) = 2 π r² + 2 π r h square units
                                                            = 2 x 3.14 x 6² + 2 x 3.14 x 12
                                                            = 2 x 3.14 x 36 + 2 x 3.14 x 12
                                                            = 226.08 + 75.36
                                                            = 301.44
Surface area of the cylinder (A) = 301.44 cm²

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The volume of the cylinder (V) = π r² h cubic units
                                                        = 3.14 x 6² x 12
                                                        = 3.14 x 36 x 12
                                                         = 1356.48

The volume of the cylinder (V) = 1356.48 cm³