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Formula for surface area and volume of cylinders

NL.SO.1201AN1

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Understanding the number systems

Prime factorization

Number properties: Prime or Composite

Number properties: Prime?

Prime factors – Word Problem

Greatest common factors (GCF)

Greatest Common Factor 2 Numbers

Greatest Common Factor 2 Numbers – Word Problem

Least common multiple (LCM)

Lowest Common Multiple - 2 Numbers – Word Problem

Lowest Common Multiple 2 Numbers

Square and square roots

Square Root of a Perfect Square

Cubic and cube roots

Cube root of a perfect cube

NL.SO.1201AN2

Evaluating and simplifying radicals

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Converting radicals to mixed radicals

Converting radicals to entire radicals

NL.SO.1201AN3

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

NL.SO.1201AN4

What is a polynomial?

Classifying Polynomials

Polynomial components

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

NL.SO.1201AN5

Solving polynomials with the unknown 

Solving polynomials with the unknown "b" from ax^2 + bx + c

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factoring perfect square trinomials

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Find the difference of squares

Using algebra tiles to factor polynomials

Common factors of polynomials

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

NL.SO.1201M1

Upper and lower bound

Upper and Lower Bound

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

NL.SO.1201M2

Direct variation

Identifying direct variations

NL.SO.1201M3

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

NL.SO.1201M4

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Use tangent ratio to calculate angles and sides (Tan = o / a)

NL.SO.1201RF1

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

NL.SO.1201RF2

Identifying functions

Function notation

Function notation (advanced)

NL.SO.1201RF3

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

NL.SO.1201RF4

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

Rate of change

NL.SO.1201RF5

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

NL.SO.1201RF6

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

NL.SO.1201RF7

Parallel and perpendicular lines in linear functions

Applications of linear relations

Applications of linear equations

Academic Mathematics 1201

Algebra and Number

Measurement

Relations and Functions

math

Ex. 1:

Hi. Welcome to this Question Here. Okay, the question asks for the surface area and the volume of a cylinder, which is good because we do have a nice equation for these questions here. So to start off, we're going the diameter equals to 42 feet and the height is 110 feet. The units are being consistent, which is good. But we don't really use diameter that much when it comes to the equation, so we're going to change them to radius. Okay? So it's a quick calculation. Just take the 42 and divide it by 2 and you get yourself the radius to be to equal to, I'm just going to put it on the side here, to be 21 feet, 21 feet right there. So let's start off by calculating the surface area first, okay? 
So surface area. Now, the equation says its 2 pi r-squared, and plus the 2 pi r with the h. Now, some people might be wondering, so why is it the equation looks like this is? Is there any reason for this to occur? It's straightforward. If you actually unwrap the cylinder, you will see that it's a circle on the top with a rectangular shape in the middle and followed by another circle. Okay? So if you unwrap it open, that's what you see. We&apos;ve got two circles and the one rectangles. That 2 pi r-squared -- the pi r-squared is the area of the circle, and since there are two of them, that's why we&apos;ve got the two here. The 2 pi r over here is the circumference of the circle, because when you unwrapped it, the length of the rectangle over here is the circumference. That's where the 2 pi r comes in. And the height is just this guy right here. Okay? 
So that's where you get the equation from. So the rest of the work to find the surface area, just plug it in. So here we go really quickly, we&apos;ve got 2 pi times the radius. That's why we had to find the radius first. We're going to square that, plus the 2 pi times the radius, 21 times the height is 110. And just use your calculator. Punch it in. You should get the answer. It turns out to be 17285 and we&apos;ve got feet, and it's a square. Okay? 
Quickly, let's do the next part, which is the volume. The volume of the cylinder is also called with the equation itself. It's just the area of the base times the height. So we're going to put down the base area, and we're going to say times the height, just like that. Now, if you look at the diagram of the cylinder, the base is the circular part, which is the bottom, right here. Okay? Or on the top, this piece right here. Identical piece. So it's a circle. Therefore the area of the circle is going to be a pi r-squared, and the height is given on the side, 110. So let's quickly fill in the information that we have. Here's my pi. The radius is 21 squared, and times the h, 110, and your answer now would be 152398.7 and we&apos;ve got ourselves the feet cubed. Remember that volume's are in cubes, the surface area are in squares. Okay? And that's your answer, right here. Thanks for watching.

A cylinder is like stacking up a pile of circle plates. With information such as, height, <a href='[[glossary.html|{"keyword":"Radius of a Circle or Sphere"}]]'>radius</a>, and circumference, it is easy to calculate the surface area and volume of cylinders.Let's look at how to calculate the surface area and volume of composite solids too.

Surface area of cylinders

Volume of cylinders

Circles and circumference 

Arcs of a circle