How to Calculate Area, Radius, Diameter, Circumference of Circle?

About this Tutorial:

Find How to Calculate Area, Radius, Diameter, Circumference of Circle with known single value of a circle

How to calculate, If you know a circle has an Area (A) of 19.6 square units, you can calculate Radius (r), Diameter (D), and Circumference (C) as follows:

Radius (r) = √ (A ÷ π)
Radius (r) = √ (19.6 ÷ 3.14159)
Radius (r) = √ (6.238879038957981)
Radius (r) = 2.4977737626138796

Circumference (C) = π * (r * 2)
Circumference (C) = 3.14159 * (2.4977737626138796 * 2)
Circumference (C) = 3.14159 * (4.995547525227759)
Circumference (C) = 15.6939754059142

Diameter (D) = r * 2
Diameter (D) = 2.4977737626138796 * 2
Diameter (D) = 4.995547525227759

How to calculate, If you know a circle has a Circumference (C) of 15.7, you can calculate Area (A), Diameter (D), and Radius (r) as follows:

Diameter (D) = C ÷ π
Diameter (D) = 15.7 ÷ 3.14159
Diameter (D) = 4.997465213085514

Radius (r) = D ÷ 2
Radius (r) = 4.997465213085514 ÷ 2
Radius (r) = 2.498732606542757

Area (A) =  π * r * r;
Area (A) =  3.14159 * 2.498732606542757 * 2.498732606542757
Area (A) =  7.84999336938866 * 2.498732606542757
Area (A) =  19.61505096136064 square units

How to calculate, If you know a circle has a Diameter (D) of 6, you can calculate Area (A), Circumference (C), and Radius (r) as follows:

Radius (r) = D ÷ 2
Radius (r) = 6 ÷ 2
Radius (r) = 3

Circumference (C) = π * (r * 2)
Circumference (C) = 3.14159 * (3 * 2)
Circumference (C) = 3.14159 * (6)
Circumference (C) = 18.84955592153876

Area (A) =  π * r * r;
Area (A) =  3.14159 * 3 * 3
Area (A) =  9.424769999999999 * 3
Area (A) =  28.274333882308138 square units

How to calculate, If you know a circle has a Radius (r) of 4, you can calculate Area (A), Diameter (D), and Circumference (C), as follows:

Diameter (D) = r * 2
Diameter (D) = 4 * 2
Diameter (D) = 8

Circumference (C) = π * (r * 2)
Circumference (C) = 3.14159 * (4 * 2)
Circumference (C) = 3.14159 * (8)
Circumference (C) = 25.132741228718345

Area (A) =  π * r * r;
Area (A) =  3.14159 * 4 * 4
Area (A) =  12.56636 * 4
Area (A) =  50.26548245743669 square units

Cramer's Rule to Solve a System of 3 Linear Equation with Step by Step Example

How to Solve a System of 3x3 Matrix Equations using Cramer's Rule with Step by Step Example

Cramer's Rule Matrix method can be used to solve systems of linear equations involving two or more variables.

Example:
3x + 2y - z = 3
x - y + 2z = 4
2x + 3y - z = 3

Solution:

Given matrix

	x	y	z	b
1	3	2	-1	3
2	1	-1	2	4
3	2	3	-1	3

Write down the main matrix and find its determinant,

	x	y	z
1	3	2	-1
2	1	-1	2
3	2	3	-1

Determinant D = -10

Replace the 1st column of the main matrix with the solution vector and find its determinant

	x	y	z
1	3	2	-1
2	4	-1	2
3	3	3	-1

D1 = -10

Replace the 2nd column of the main matrix with the solution vector and find its determinant

	x	y	z
1	3	3	-1
2	1	4	2
3	2	3	-1

D2 = -10

Replace the 3rd column of the main matrix with the solution vector and find its determinant

	x	y	z
1	3	2	3
2	1	-1	4
3	2	3	3

D3 = -20

x1 = D1 / D = -10 / (-10) = 1

x2 = D2 / D = -10 / (-10) = 1

x3 = D3 / D = -20 / (-10) = 2

Solution:

x = 1

y = 1

z = 2

Gauss Jordan Matrix Equations Elimination Method Step by Step Example

Jordan Matrix Elimination Method Step by Step Example

Jordan Matrix method can be used to solve systems of linear equations involving two or more variables.

Example:
3x + 2y - z = 3
x - y + 2z = 4
2x + 3y - z = 3

Solution:

Given matrix

	x	y	z	b
1	3	2	-1	3
2	1	-1	2	4
3	2	3	-1	3

Find the pivot in the 1st column and swap the 2nd and the 1st rows

	x	y	z	b
1	1	-1	2	4
2	3	2	-1	3
3	2	3	-1	3

Multiply the 1st row by 3

	x	y	z	b
1	3	-3	6	12
2	3	2	-1	3
3	2	3	-1	3

Subtract the 1st row from the 2nd row and restore it

	x	y	z	b
1	1	-1	2	4
2	0	5	-7	-9
3	2	3	-1	3

Multiply the 1st row by 2

	x	y	z	b
1	2	-2	4	8
2	0	5	-7	-9
3	2	3	-1	3

Subtract the 1st row from the 3rd row and restore it

	x	y	z	b
1	1	-1	2	4
2	0	5	-7	-9
3	0	5	-5	-5

Make the pivot in the 2nd column by dividing the 2nd row by 5

	x	y	z	b
1	1	-1	2	4
2	0	1	-1.4	-1.8
3	0	5	-5	-5

Multiply the 2nd row by -1

	x	y	z	b
1	1	-1	2	4
2	0	-1	1.4	1.8
3	0	5	-5	-5

Subtract the 2nd row from the 1st row and restore it

	x	y	z	b
1	1	0	0.6000000000000001	2.2
2	0	1	-1.4	-1.8
3	0	5	-5	-5

Multiply the 2nd row by 5

	x	y	z	b
1	1	0	0.6000000000000001	2.2
2	0	5	-7	-9
3	0	5	-5	-5

Subtract the 2nd row from the 3rd row and restore it

	x	y	z	b
1	1	0	0.6000000000000001	2.2
2	0	1	-1.4	-1.8
3	0	0	2	4

Make the pivot in the 3rd column by dividing the 3rd row by 2

	x	y	z	b
1	1	0	0.6000000000000001	2.2
2	0	1	-1.4	-1.8
3	0	0	1	2

Multiply the 3rd row by 0.6000000000000001

	x	y	z	b
1	1	0	0.6000000000000001	2.2
2	0	1	-1.4	-1.8
3	0	0	0.6000000000000001	1.2000000000000002

Subtract the 3rd row from the 1st row and restore it

	x	y	z	b
1	1	0	0	1
2	0	1	-1.4	-1.8
3	0	0	1	2

Multiply the 3rd row by -1.4

	x	y	z	b
1	1	0	0	1
2	0	1	-1.4	-1.8
3	0	0	-1.4	-2.8

Subtract the 3rd row from the 2nd row and restore it

	x	y	z	b
1	1	0	0	1
2	0	1	0	0.9999999999999998
3	0	0	1	2

Solution set:

x1 = 1

x2 = 0.9999999999999998

x3 = 2

Calculate Eccentricity (e), Foci, X Y Intercept, Major, Minor Axis of Ellipse?

Calculate Eccentricity (e), Foci, X Y Intercept, Major, Minor Axis of Ellipse for 3x² + 4y² = 5 Equation?

Given an ellipse with equation 3x² + 4y² = 5 determine the following:

• x and y intercepts
• Coordinates of the foci
• Length of the major and minor axes
• Eccentricity (e)

3x2 + 4y2 = 5
5

     3x² + 4y² = 5             3x²                     4y²

= ----------------- = -------------------- + -------------- = 1

             5                1.66666666667         1.25

To determine a and b, we need the square roots of the bottom portions of the fractions:

             3x²                           4y²

= -------------------- + ---------------------- = 1

   1.29099444874²     1.11803398875² 

Calculate x intercept by setting y = 0:

x² = 1.66666666667 x 1
x² = 1.66666666667
x = √1.66666666667
x = ± 1.29099444874

Calculate y intercept by setting x = 0:

y² = 1.25 x 1
y² = 1.25
y = √1.25
y = ± 1.11803398875

Calculate the foci

The equation relating a, b, and c is c² = √a² - b²

Since a must be greater than b, a = 1.29099444874 and b = 1.11803398875

c² = √1.66666666667² - 1.25²

c² = √0.416666666667

Foci Points are (0,√0.416666666667) and (0,-√0.416666666667)

Calculate length of the major axis:

Major axis length = 2 x a

Major axis length = 2 x 1.29099444874

Major axis length = 2.58198889747

Calculate length of the minor axis:

Minor axis length = 2 x b

Minor axis length = 2 x 1.11803398875

Minor axis length = 2.2360679775

Calculate eccentricity (e):

e  =	√a2 - b2
	√a2

e  =	√1.666666666672 - 1.252
	√1.666666666672

e  =	√2.77777777778 - 1.5625
	√2.77777777778

e  =	√1.21527777778
	√2.77777777778

e  =	1.10239637961
	1.66666666667

e = 0.661437827766