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Master Surface Area and Volume of Prisms: Key Geometry Skills

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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Ex. 1

Intro

- Hi, so welcome to this question here. Well, we're trying to find the surface area and the volume for this question here. It looks like a simple one but it's not, okay. Because it's different shapes, different lengths and the width for the different dimensions here. So we'll start off by figuring out the surface area, okay? 
So to figure out the surface area, that means you get the front and the back, you get the bottom piece, you get the slanting side right here. You also get the side over here which is the left side, okay? So a couple of things we should check before we start the question, it's to check all the dimensions to see that they all have the same units for all of them. We get the millimeter, millimeter and the centimeter. So I'm going to change this centimeter into millimeter first. But we know that for every centimeter, it's just a 10 millimeter, right? So I'm just going to change this number to 12 millimeters right away. So just let me change a color panel here, so I'm going to change it into 12 millimeter here so you won't forget, okay? Let me erase that quickly, 12 millimeters. Okay. So coming back over here. So then once now we've changed it, we need one more dimension that's not given to us. Okay, because if we're going to calculate the surface area, eventually we&apos;ve got to calculate this side right here. So we need the dimension of this side right here, this slanting side, okay? So we need a little bit of math which is called the pythagoras. So we need to figure out this slanting side here which we called the 
"S", okay? 
So that is a right triangle right here. That means you could use the C-square equals A-square plus the B-square. Okay? 
Let me see if we can find a little space right here to show you the work, so let me sign in red. So coming down over here, let's just kind of do the equation S-square equals to A-square plus the B-square, okay? So to find the S, you're going to square root whatever you have for the two sides. So looking for this one right here, so we&apos;ve got the 16 and 12, 16 and the 12 okay? So if you do the math, you're going to figure out the slanted side is going to turn out to be-- it's approximately 20, okay? So let's just use 20 over here, and let me just put equals to 20 over here as well. Okay? So now once we have all the dimensions, we're now ready to go ahead and calculate all the surface area that we have. All right? 
So to start off is really up to you. You can calculate area here, the top, the front, the back, it doesn't matter. I'm just going to follow my work right here. I'm going to do the front and the back which is this side right here and the ones in the back. Okay? So I'm going to call in the F and the B. So the front part of triangular prism here is actually triangular shape, right? So you're going to use the base times the height divided by two equation. So we're going to do the base times the height divided by two to find the front part. But since there's two identical pieces, so you're going to multiply it by two anyway. So to save yourself a work, two divided by two, that part is gone. So just take the base which is the 12, okay? Just going to multiply it by the 16, okay? So we&apos;ve got a nice number on the side right here, it's going to give us 192, okay. It's the millimeter square, that's the 192 over here. Then we're going to look at what other shapes that we have. So we still have the bottom piece. So let's say we're going to do the bottom piece right now. So let's come down to here for the bottom piece. Let me fill in the whole work here for you. Okay? Now if you look at the bottom piece, it's actually going to be a rectangular shape. We can actually draw a little bit of lines in there to show you that the shape is going to look like something like this, right? Okay, and I believe this one is down this way. Okay, and that's it. So it's a rectangular piece. So that means you just going to take the length times the width for the area calculation. Okay? 
So coming back over here, it's just going to be the length times the width. So we&apos;ve got the length right here, it's actually 12 times 12. So it's actually a cube. So it's 12 times 12, let's just square that number right there. So we&apos;ve got 144 millimeter square. Okay, the 144. Then what else do we have? We still got the left side which is nice and easy to calculate because we do have the dimension already. If this is 12, that's going to be 12 right here, and that's 16. So let's say we do the one on the left. So this is the left, okay? To find the surface area, again it's just the length times the width. So we&apos;ve got the 12 and the 16. So let's put down 12 times 16. A little messy here, let me get it erased right there, 12 times 16 and my answer to that part right there would be 192. Okay, so 192 meter square. Okay? 
So coming down to the last side, okay it's a little bit of more work because every side is a little different. So this slanted side right here. Now remember the reason we'll be calculating the S is so that we can get the surface area because the length is 12 here and then the height will be 20, okay? So let's call it a slanted side right there, the slanted. We&apos;ve got the length times the width again. You can put in any number you like in any order because we're doing multiplication anyway, 20 times the 12. We&apos;ve got a nice number right here, it's 240 centimeter square. So at the end, to get all the surface area all you have to do is just add everything together. So if you punch it in a calculator, you should get a nice number which going to give you 768, okay? Don't forget the unit, square. Okay? Now, coming back to the very last part of the question, it's to find the volume. Now, the volume it's much, much easier because there's-- use the equation, right? 
So I'm going to put a little space right here. To figure the volume of a rectangular prism is equation is just the base of the area, the base area actually. I'm just going to call it the base area, and multiply it by the height of that triangle which is going to be the 16, okay? So multiply it by the height. So the base area is going to be 12 times the 12, and the height is going to be the 16, okay? So we&apos;ve got to take-- Oh sorry, it's not the base. Sorry, my bad. It's actually the triangular part is your base, okay? It's the 12 times the 16 divided by two. So we&apos;ve got 12 times the 16 divided by two because you're doing a triangular prism. The base is not the rectangular part, it's the triangular part. My bad. So it's the 12 times 16 divided by two and then you multiply it by the height. Now the height, if you would treat this side as a base, then the height is going this way, okay? Then the 12 is the height in this question, okay? So the volume for this one at the end is going to be 1,152 millimeter cube. Okay? 
That's it for this question. Thanks for watching.

So, we've learned the basics in the "Introduction to volume" lesson. Now, let's practice some harder questions on how to find out the surface area and volume of prisms and composite solids. 

Finding the surface area and volume of prisms

Volume of prisms