A Three Dimensional Figures

Introduction of three Dimensional Figures:

        Three Dimensional figures which are the solid shapes consist of 3 sides that mean length, width, depth. In geometric three dimensional figures contains side, vertex and edges.

Face or Side is nothing but the plane or flat surface.

Vertex represents the corner of that solid three dimension figure.

Edge is denoted as the place of three dimensional figure where faces meet.

 three dimensional figures

Let us see the example of 3 dimensional figures.

 

Properties of three dimensional figures

 

Sphere – Consists of no plane sides, no narrow edges with only one curved side.

 Sphere

Cone – Consists of one curved side and one plane side and its plane surface is nothing but the circle.

 Cone

 

Cube – consisting of 6 flat square surfaces and 12 straight edges and 8 corners.

 Cube

Cylinder – Consists of one curved surface and 2 flat circular surfaces.

 Cylinder

Prism – cross sectional: Where ever its cut prism gives the similar shapes.

 Prism

Pyramid: All the sides are meeting at a point.                                  

 Pyramid

 

Formula used in 3 dimensional figures :

 

Formula for finding the volume of the cone:

The volume of the conic figure is defined as the one by third of area of base and height ( h ) of the cone.

V = `1/3` A . h

A = area of the circlular base = `pir^2`

 

Surface Area of cylinder can be calculated as,

Area of two circular base + Area of curved side.

2Пr2 + 2Пrh

Volume of Cylinder – Пr2h.

Where ,

r is denoted as the radius of the flat surface.

h is denoted as the height of the cylinder.

 

Examples on three dimensional figures

 

Ex 1: Find the surface area of the cylinder when the area of the cylinder is 157 cm2 and the radius and height is 5 cm and 7 cm respectively.

Sol: Given: Area = 157 cm2

Radius = 5 cm

Height = 7 cm

Formula: 2Пr2 + 2Пrh = 157 + 2П5(7) =157 + 219.8 = 376.8 cm2

 

Ex 2:Find the volume of the cylinder whose radius and height 4 cm and 3 cm respectively.

Sol: Given:

Radius = 4 cm

Height = 3 cm.

Formula: πr2h = π(4)2(3) = 150.72 cm3

Ans: 150.72 cm3