Geometry Solid Figures

Geometry solid figures are a branch of geometry which mainly focuses on the properties like surface area, and volume of solid figures or three dimensional shapes like Rectangular Prism, cube, cone, cylinder, and sphere. Geometry solid figures generated by the revolution of a two dimensional plane. For example a cylinder is generating by the revolution of a rectangle; the revolution of a circle about its diameter generates a sphere.

Formulas for geometry solid figures:-

Geometry solid figures of Cube:-


Surface area = 6a2 square units, Volume = a3 cubic units.

Geometry solid figures of Cylinder:-


Lateral surface area = 2πrh square units, Total surface area = 2πr (h + r) square units, Volume = πr2h cubic units

Geometry solid figures of Cone:-


Lateral surface area = πrs square units, Total surface area = πrs + πr2 square units, Volume = 1/3 πr2h cubic units

Geometry solid figures of Sphere:-


Surface area of a sphere = 4πr2 square units, Volume = 4/3 πr3 cubic units

Geometry solid figures of Rectangular Prism:-


The equation for find the volume (V) of a rectangular prism is V = wdh.

Example geometry solid figures problems:-

Example problem1:-

Find the volume of cylinder given the radius is 6 cm and 11 cm.

Solution:-

Volume of cylinder = r2 h cubic units.

= (3.14) * 62 * 11

= 3.14 * 36 * 12

= 1 356.48cm3

Example problem2:-

Find the volume of cone given the radius is 4 cm and 8 cm.

Solution:-

Volume of cone = 1/3 r2 h cubic units.

= 1/3 (3.14) * 42 * 8

= 0.33 * 3.14 * 16 * 8

= 132.6336cm3

Example problem3:-

Find the volume of cube with the side length of 8 cm.

Solution:-

Volume of cube = a3

= 83

= 512 cm3

Example problem4:-

A rectangular prism contains at width for 3 inches and depth 6 inches and height 4 inches then finds the volume of rectangular prism?

The faces are known as width (w), depth (d), and height (h).

Solution:-

Volume (V) of a rectangular prism is:

V = wdh.

Now we can calculate,

V= wdh

V= 3 in x 6 in x 4 in

V = 72 in3

Example problem5:-

The sphere has the radius of 4m.find the surface area of the sphere.

Solution:-

Radius (r) = 4 m

Surface area of the sphere = 4 π r2 square unit

= 4 x 3.14 x (4)2

=4 x 3.14 x 16

= 200

Surface area of the sphere =200 m2.