Solving Geometry Explanation

Introduction :-

In geometry, an arc is a segment of a differentiable curve in the two-dimensional plane; for example, a circular arc is a segment of the circumference of a circle. If the arc segment occupies a great circle (or great ellipse), it is considered a great-arc segment.I like to share this Math Pythagorean Theorem with you all through my article.
(Source : Wikipedia)

Example Problems for Solving Geometry Explanation

Problem 1:-

Solving geometry explanation to find the volume of cone with radius 7 cm and height 8 cm.

Solution:

Given: Radius = 7 cm

Height = 8 cm.

Volume of cone = (`1/3` ) * `pi` * radius2 * height

= (`1/3` ) * 3.14 * 72 * 8  ( multiplying these values)

= 0.33 * 3.14 * 49 *9  ( multiplying the values)

= 456.96 cubic cm.

The volume of cone is 456.96 cubic cm.

Problem 2:

Solving geometry explanation to find the Perimeter of Parallelogram for the side of a 8 and side of b is 6.

Solution:

Given: Side a = 8

Side b = 6

Perimeter of Parallelogram P = 2 * 8 + 2 * 6  ( multiplying the values)

P = 16 + 12

P = 28

The Perimeter of Parallelogram is 32

Problem 3:

Solving geometry explanation to find the circle area and circumference radius with 6 cm.
Solution:

Given: Radius = 6 cm

Area of Circle = `pi` * radius2          `pi` = 3.14

= 3.14 * 62

= 3.14 * 36   ( multiplying the values)

= 113.04 square cm.

The Area of Circle is 113.04 square cm

Circumference of Circle = 2 * `pi` * radius

= 2 * 3.14 * 6   ( multiplying the values)

= 37.68cm.

The Circumference of Circle 37.68 cm

More Example Problems for Solving Geometry Explanation

Problem 1:

Solving geometry explanation to find the Area of Triangle with height 3 cm and Base 7 cm.

Solution:

Given: Height = 3 cm

Base = 7 cm

Area of Triangle = (½) * height * base

= 0.5 * 3* 7   ( multiplying these values)

= 10.5 square cm.

The Area of Triangle 10.5 square cm

Problem 2:

Solving geometry explanation to find the Area of rhombus whose diagonal lengths are 5 cm and 8 cm.

Solution:

Area of Rhombus = (½) * Length of the diagonal 1 * Length of the diagonal 2

= `1/2` * 5* 8 ( multiplying these values)

= 20 square cm.

The Area of Triangle 20 square cm

Line Segments in a Pentagon

Introduction to line segments:

The division of a line with two end points is called a line segment. Line segment RS which we denoted by the symbol `bar(RS)` .



Note: We shall denote a line segment `bar(RS)` by RS only.

From the above figure, we call it a line segment RS. The points R and S are called end-points of the line segment RS.

We can also name it as line segment RS.

A line segments:

(a) A line segment has a definite length.

(b) A line segment has two end-points

Line Segments in a Pentagon:
Find the line segments of the given pentagon. The pentagon shown below figure,



Solution:

Given:

Pentagon EFGHI

To find the line segments in a pentagon:

We know that the line segments are consisting of two end points. Here, the pentagon has five end points, such as E, F, G, H, and I. The five end points to form the line segments in a pentagon by connecting these end points shown in figure, such line segments are EF, FG, GH, HI, and IE. These line segments are represented by `bar(EF)` , `bar(FG)`, `bar(GH)` , `bar(HI)` , and `bar(IE)` . Therefore, the given pentagon has five line segments.Please express your views of this topic Converting Fractions to Percents by commenting on blog.

Line Segments in a Solid Pentagon:

Find the line segments of the given solid pentagon. The solid pentagon shown below figure,



Solution:

Given:

Solid pentagon ABCDEFGHIJ

To find the line segments in a solid pentagon:

We know that the line segments are consisting of two end points. Here, the pentagon has ten end points, such as A, B, C, D, E, F, G, H, I, and J. The ten end points to form the line segments in a solid pentagon by connecting these end points shown in figure, such line segments are AB, AD, AJ, BC, BF, CD, CE, DI, EF, EG, FH, GH, GI, HJ, and IJ. These line segments are represented by `bar(AB)` , `bar(AD)` , `bar(AJ)` , `bar(BC)` ,` bar(BF)` , `bar(CD)` , `bar(CE)` , `bar(DI)` , `bar(EF)` , `bar(EG)` , `bar(FH)` , `bar(GH)` , `bar(GI)` , `bar(HJ)` , and `bar(IJ)` . Therefore, the given solid pentagon has fifteen line segments.

Radius of a Circle from Circumference

Radius of a circle from circumference:
The terms radius, diameter and circumference are related to two-dimensional geometric shape named circle. Circle is a two dimensional closed shape with curved edges. The distance between the center of the circle and any point on  the circle  is always same. Circumference of the circle is 2pi r  .where, r is the radius of the circle .

Here radius is the distance between the center of the circle to any point on the circles. Circumference is the total distance around the circle. Let us discuss about the radius from the circumference of the circle,



Example Problem to Find Radius from Circumference:

Example 1:

Find radius of the circle if circumference is 34cm.

Solution:

The classic formula for circumference is `2 pi r`

Therefore,

Circumference =2`pi` r =34cm

Simplify it for radius (r) we get ,

Radius r=`34/2pi`

We know that `pi ` =3.14 or` 22/7`

Therefore, r= `34/(2*3.14)`

=5.41cm

Therefore value of radius from circumference is 5.41cm

Example 2:

Find radius of the circle if circumference is 23cm.

Solution:

The classic formula for circumference is `2 pi r`

Therefore,

Circumference =`2pir` =23cm

Simplify it for radius (r) we get ,

Radius `r=23/2pi`

We know that pi =3.14 or `22/7`

Therefore,` r= 23/(2*3.14)`

=3.66cm

Therefore, value of radius from circumference is 3.66 cm

Example 3:

Find radius of the circle if circumference is 72.4cm.

Solution:

The classic formula for circumference is` 2 pi r`

Therefore,

Circumference =`2pir ` =72.4cm

Simplify it for radius (r) we get ,

Radius r=`72.4/(2pi)`

We know that `pi` =3.14 or `22/7`

Therefore, r=`72.4/(2*3.14)`

=11.52 cm

Therefore, value of radius from circumference is 11.52cm

Example 4:

Find radius of the circle if circumference is 11cm.

Solution:

The classic formula for circumference is `2 pi r`

Therefore,

Circumference =`2pir` =11cm

Simplify it for radius (r) we get ,

Radius r=`11/2pi`

We know that pi =3.14 or `22/7`

Therefore, r= `11/(2*3.14)`

=1.75cm

Therefore, value of radius from circumference is 1.75 cm

Example 5:

Find radius of the circle if circumference is 28inch.

Solution:

The classic formula for circumference is `2 pi r`

Therefore,

Circumference =`2pir ` =28inch

Simplify it for radius (r) we get ,

Radius` r=28/(2pi)`

We know that `pi` =3.14 or `22/7`

Therefore, r= `28/(2*3.14)`

=4.45inch

Therefore, value of radius from circumference is 4.45inch

Is this topic how to measure volume hard for you? Watch out for my coming posts.

Practice Problem to Find Radius from Circumference:

1) Find radius of the circle if circumference is 12cm.

Answer:1.91cm

2)Find radius of the circle if circumference is 44cm.

Answer:7cm