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Finding the surface area of 3 dimensional shapes

PAT: Master Provincial Achievement Test Skills

Operations with Decimals

test

Adding and subtracting decimals

Subtracting Decimals — Data Table

Ordering Decimals — Data Table

Decimals – Word Problem

Adding Decimals

Subtracting Decimals

Multiplying decimals

Multiplying Decimals

Dividing decimals 

Dividing Decimals

Order of operations (BEDMAS)

Mixed Operations with Decimals

Mixed Operations

Identify the Order of Operations

Order of Operations — Word Problem

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Rational Numbers

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Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

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

Introduction to Linear Relations

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Linear Relations

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

Model and solve one-step linear equations: ax = b, x/a = b

One-step Linear Equations

One Step Linear Equations — Word Problem

One-step equations

One-step Equations LHS

One-step Equations RHS

Model And Solve One Step Linear Equations Divide – Word Problem

Model And Solve One Step Linear Equations Multiply – Word Problem

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

Solving two-step linear equations using multiplication and division: x/a + b = c

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

Solve Linear Equations Using Distributive Property – Word Problem

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

What is a polynomial?

Classifying Polynomials

Polynomial components

Operations with Polynomials

Adding and subtracting 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

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Surface Area of 3D Objects

Surface area of 3-dimensional shapes

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

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Symmtery

Line symmetry

Rotational symmetry and transformations

Influencing factors in data collection

Data collection

Probability

Provincial Achievement Test

sample

math

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- Hi, welcome to this question right here. So what happen is we're trying to determine the dimension of this cut out piece. So we&apos;ve got a little rectangle right here, right? So we&apos;ve got all sort of information down here, so we're going to use each pieces right here to determine the dimension of this part that you're going to cut out which is this part right here. Okay? 
So let's start from the top first. So if you're looking from the top, it says now right over here on the back over here is 20. So I'm going to put a little 20 right there to remind our self, and this part right here. This part here is 15, so that's 15. Okay? So that's going to add it in. So far there isn't too much information that we have to determine the dimension of that little cut out piece. Let's go to the next one, just looking it from the left. So this is your left and side, this piece right here. That's your left hand side. So it says, if you're looking from the left. This part right here is six centimeters, so that six. So we just discovered our first dimension to the cut out piece. This bottom part right here is six. Okay? 
Then, we have nothing else. Okay, that's unfortunate but we do know that 20, that's 20, that's six. So then makes this part here 14. Okay? I don't know if we need that but, let's just put it in just in case we needed that for a later questions. Let's focus on the front. If you're looking from the front, you're looking from this way, okay? So we have the 20-- 
This side is also 20, okay. So I'm going to put a little line right there to represent that as side 20. We know that the bottom part is 27. That's your 27. We do know the next dimension now, because it looks like-- actually we do, because that's 10 right there. See this part right here, the 10? That means this part here is also 10. Okay? I kind of ran out of space, but if you just do a quick math right there. This whole thing is 20, right? That part is 10. So that makes this part here as 10 as well. Okay? That part represents this part here. So we just found out that our next dimension which is this part, that's 10. This is also 10. Okay? 
So the only thing that we're missing is actually-- 
Oh, it's not missing, it's actually-- We know this side, the whole thing is 27, right? Now, if you take that 27 and subtract the 15 on the top, you get yourself just the 12. Okay? That 12 will go right there. So we just figure out our last dimension right here which is 12, okay? So six times 12, times 10 for this cut out piece and if you want to figure out the area right now. Six time 12 times the 10, we&apos;ve got our area turns out to be-- 
Just let me fill the work here, which is length times the width times the height, right? So we&apos;ve got ourselves six times the 12, times the 10. We have 720, okay? 
So that 720 is the area and the dimension for this question, it's six time 10, times the 12. Then let's quickly go to the next question and see what they're asking for. They're looking for-- Just let me see, so I'll remember it. We still have the dimension of 720, right? But as you can see, the next question says, "How does the surface area of the original rectangle object change after cutting out that corner piece?" 
Well, this question here doesn't really need the calculation because if you think about it, the surface area did not change at all. Okay? So the answer to that question right now, I want to say there's no change. Now, you'll probably thinking like, "Okay, how is that possible?" 
Because you cut out a one piece from the original rectangle, right? This piece has been cut out, but surface area is different from the volume. Surface area is we look at an object from all the surfaces, right? So if you just imagine, if you look at this cut out pieces right now, then other cut out piece, this diagram right here with all these dimensions. If you're looking from the top, you still see a perfect rectangle. If you look at it from the left that it's still a perfect rectangle. If you see it from the right which is still a rectangle, right? When you're seeing right here, it's the same as before. Okay, because when you look at it from-- 
Let's say if you're looking from the top, you still see the surface-- Let me just erase all these right here. You still see all the surface area, including that little piece down here. So the surface area actually didn't change from before and after. So that's why the surface area of the original rectangle object did not change even after you cut it out, okay? 
Only the volume changes, okay? Hoping that it make sense. Thanks for watching.

In this section, we will learn how to calculate the surface area of 3D objects. We will also look further into the subject ? What would happen to the surface area if the shapes are 
cut into pieces? How about a piece is cut out of the shape? 