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Master Surface Area of Cylinders: Formulas & Examples

EQAO Grade 9 Math: Master Core Concepts & Skills

Ratios, Rates, and Proportions

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Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Pythagorean Theorem

Introduction to pythagorean theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Rational Numbers

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Mixed Operations with Decimals

Mixed Operations

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Solving problems with rational numbers in fraction form

Operations with fractions

Determine square roots of rational numbers

Square roots of rational numbers

Powers and Exponents

Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Proportional Relationships

Understanding graphs of proportional relationships

Linear relations

Using tables of values to graph proportional relationships

Linear relation

Applications of proportional relationships

Identifying proportional relationships

Linear Ralations

Representing patterns in linear relations

Represent Patterns in Linear Relations Equation Decimal

Represent Patterns in Linear Relations Equation Integer Start From 0

Represent Patterns in Linear Relations Equation Integer Start From 1

Represent Patterns in Linear Relations Equation Negative Decimal

Identify the Linear Equation

Reading linear relation graphs

Solving linear equations by graphing

Solving Linear Equations

Solving linear equations using multiplication and division

Two-step Linear Equations LHS

Two-step Linear Equations RHS

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Linear Functions

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>

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

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

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

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Multiplication and Division of Polynomials

Multiplying and dividing monomials 

Divide a monomial by a monomial

Multiply a monomial by a monomial

Multiplying polynomials by monomials

Multiply a polynomial by a monomial

Dividing polynomials by monomials

Introduction to 3-Dimensional Objects

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

Surface Area and Volume

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

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Data Management

Influencing factors in data collection

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Scatter plots and correlation

Census and bias

Census and Bias

Classifying Bias

Linear Programming

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

EQAO Grade 9 Principles of Math

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Intro

- Hi, welcome to this question right here. So we're going to find the surface area of the cylinder. Now there is an equation for this because what happened is if you unwrap the cylinder open, technically it looks like you have a circle on the top and followed by a rectangular piece in the middle. Another circle at the end. Because that's the top, bottom and that's the middle piece. So the equation for the surface area for your cylinder is actually the pi R square, this part here refers to the area of the circles. This one right here, but we have two identical circles here. So you just need to a two in the front. So the two pi R square will give you the area of the circles here and here. Now what about the one in the middle? The one in the middle, you add on top of that. The one in the middle happens to be a rectangle. Now we already know the height here is seven, because that is the height right there. So it's just going to be the height but it's going to multiply this side right here which is the length, but where's the length? Imagine if you wrap it around the circle, that wrapping around the circle is actually the circumference. So the length over here, I'll write that down, is actually just the circumference which is the C, and C equals to, the two pi R okay? So at the end, we're not taking the length times the width. It's actually the two pi R times the width. So I'm going to put down the two pi R right here, and I'm just going to times the height in this equation here. So literally this is the equation to calculate the surface area of any cylinder. Okay? 
So there you go. We're going to plug the numbers in. I got the two times the pi, times the radius. I was given the radius, it was three centimeters. I got to square that, plus the two pi times this three, and times the height which is seven. All you have to do is grab your calculator and just punch everything inside. We're going to get some decimals, but it's fine. Two times pi. So we have two times pi and times three squared, and plus two times the pi, times this three times 21, okay? Now we have 60 pi, okay? If you're looking for like the exact value of answers, this is the final answer for your-- like the exact numbers which is 60 pi, okay? But if you don't want it, you want some decimals, then it's going to get you the 188.50 centimeter square, and this is your final answer for this question. Thanks for watching.

As long as we have the diameter or <a href='[[glossary.html|{"keyword":"Radius of a Circle or Sphere"}]]'>radius</a> and the height of the cylinder, we are able to find its surface area in no time. The surface area of a cylinder is basically adding the surface are of a rectangle and two circles together. The most difficult part is to find the circumference of the circles, which is also one of the sides of the rectangle.

How to find the surface area of cylinders

Circles and circumference 

Areas and sectors of circles