Formula Math Of Cylinder

Mathematics formula math of Cylinder :

Definition of A cylinder as a solid figure that is bound by a curved surface and two flat surfaces. The surface area of a cylinder can be found by breaking it down into 2 parts:

1.  The two circles that make up the caps of the cylinder.
2.  The side of the cylinder, which when "unrolled" is a rectangle.

 Formula Math :
The area of each end cap can be found from the radius r of the circle, which is given by:
A = πr²

Thus the total area of the caps is 2πr².

The area of a rectangle is given by:
A = height × width

The width is the height h of the cylinder, and the length is the distance around the end circles, or in other words the perimeter/circumference of the base/top circle and is given by:
P = 2πr

Thus the rectangle's area is rewritten as:
A = 2πr × h

Combining these parts together we will have the total surface area of a cylinder, and the final formula is given by:

A = 2πr² + 2πrh

Smart Math Formula Note :
π  =  Pi, approximately 3.142,  r  = the radius of the cylinder, h  = height of the cylinder

By factoring 2πr from each term we can simplify the formula to:

A = 2πr(r + h)

The lateral surface area of a cylinder is simply given by: LSA = 2πr × h.
Smart Math Formula  in the application :

• Find the surface area of a cylinder with a radius of 4 cm, and a height of 3 cm.

Smart Solution:
SA = 2 × π × r² + 2 × π × r × h
SA = 2 × 3.14 × 4² +  2 × 3.14 × 4 × 3
SA = 6.28 × 16 + 6.28 × 12
SA = 100.48 + 75.36
SA = 175.84
Surface Area = 175.84 cm²

•  Find the surface area of the cylinder with a radius of 5.5cm and height of 10cm.

Smart Solution:
The radius of cylinder = 5.5 cm.
The height of cylinder = 10 cm.
The total surface area of the cylinder is therefore:
TSA = 2πr(r+h)
TSA = 11π (5.5+10)
TSA = 170.5 π
TSA = 535.6 cm²

•   Find the total surface area of a cylindrical tin of radius 17 cm and height 3 cm.

Smart Solution:
Again as in the previous example:
TSA = 2πr(r+h)
TSA = 2π× 17(17+3)
TSA = 2π×17×20
TSA = 2136.56 cm²

•  Find the surface area of the cylinder with radius of 6 cm and height of 9 cm.

Smart Solution:
The radius of cylinder: r = 6 cm
The height of cylinder: h = 9 cm
Total surface area of cylinder is therefore:
TSA = 2πr(r + h)
TSA = 12π (6+9)
TSA = 180 π
TSA = 565.56 cm²

• Find the radius of cylinder whose lateral surface area is 150 cm² and its height is 9 cm.

Smart Solution:
Lateral surface area of cylinder is given by:
LSA = 2πrh
Given that:
LSA = 150cm²
h = 9cm
π is the constant and its value = 3.14

Substitute the values in the formula and find the value of r by isolating it from the equation:
LSA = 2πrh
150 = 2× π × r × 9
r = 150 / (2×9× π)
r = 2.65cm
So the radius of the cylinder is 2.65 cm.

That is  Smart Math aplication from Cylinder Formula Math.

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Easy Math of Linear (Equations and Inequalities) One Variable

Math of Linear (Equations and Inequalities) One Variable
Completion of the set of graphs of linear equations of the variables shown in a number line, in the form of dot (point).
example
Determine the completion of the set of equations
4 (2x + 3) = 10x + 8, if x
variables on the set of integers. Then, draw the number line
completion:
4 (2x + 3) = 10x + 8
8x + 12 = 10x + 8
8x + 12 - 12 = 10x + 8-12 (both sides minus 12)
8x = 10x - 4
8x - 10x = 10x - 4 - 10x (10x minus both sides)
-2x = -4
-2x: (-2) = -4 (-2) (both sides are divided by -2)
 x = 2
Thus, the solution set is {2}.

Easy Math of Linear Inequalities One Variable
In everyday life, surely you've come across or find sentences like the following.
a. Rebbecca weigh more than 52 kg.
b. Josh height 7 cm less than my height.
c. One of the requirements to be members of the Army is his height not less than 165 cm.
d. A bus can carry no more than 55 people.
How sentences are expressed in the form of mathematical sentence? To be able to learn to answer the following description.

1. understanding inequality
In order for you to understand the sense of inequality, try to remember back in elementary school about the matter in writing notation <,>,<,> , and not same.
a. 3 less than 5 written 3 <5.
b. 8 more than 4 written 8> 4.
c. x no more than 9 written x < 9.
d. Two times y is not less than 16 written 2y > 16.
Sentences 3 <5, 8> 4, x < 9, and  are called the inequality 2y >16 .
In general it can be written as follows.
An inequality is always marked by one of the following hyphen.
"<" For less than stated.
">" To declare over.
"<" to represent no more than or less than or equal to.
">" to represent not less than or more than or equal to.

2. Linear Inequalities One Variable
On the front you have learned that an equation is always marked with a hyphen "=". In this section you will learn the characteristics of an inequality.
example
Of the following forms, which specify a linear inequality with one variable.
a. x - 3 <5
b. A < 1 - 2b
c. x2 - 3x > 4
completion:
a. x - 3 <5
Inequality x - 3 <5 has one variable, namely x and rank 1, so x - 3 <5 is a variable linear inequality.
b. A < 1 - 2b
Inequality a < 1 - 2b has two variables, namely a and b, each of which rank 1.
Thus a < 1 - 2b is not a single variable linear inequalities.
c. x2 - 3x > 4
Due to the inequality x2 - 3x > 4 has variable x and x2, then x2 - 3x > 4 is not a single variable linear inequalities in Easy Math of Linear.

 

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