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Finding the surface area of 3 dimensional shapes

Solve problems requiring manipulation and application of formulas related to volume capacity surface area

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Solving rational equations

Applications of quadratic functions

Applications of quadratic equations

Demonstrate understanding of slope as rise over run rate of change and by solving problems

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

Slope intercept form: y = mx + b

Rate of change

Solve problems by applying proportional reasoning and unit analysis

Direct variation

Identifying direct variations

Inverse variation

Joint and combined variation

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

Solve problems involving two and three right triangles

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)

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Solve problems involving scale

Applications of linear relations

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Transformations of quadratic functions

Model and draw 3-D objects and their views

Surface area of 3-dimensional shapes

Solve problems involving SI and imperial units in surface area measurements and verify solutions

Applications of rational equations

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

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

Analyze puzzles and games involving numerical reasoning using problem-solving strategies

Arithmetic sequences

Geometric sequences

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

Rational vs. Irrational numbers

Solve problems involving personal budgets

Taxes, discounts, tips and more

Discounts — Word Problem

Taxes — Word Problem

Percentage - Applying a Discount Price– Word Problem

Percentage - Applying a Discount Percent – Word Problem

Percentage - Applying a Tax Total – Word Problem

Percentage - Applying a tax Percent – Word Problem

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

Demonstrate an understanding of compound interest

Finance: Compound interest

Finance: Compound Interest

Demonstrate understanding of financial institution services used to access and manage finances

Finance: Future value and present value

Solve problems involving creating and interpreting bar graphs histograms line graphs and circle graphs

Graphing piecewise linear functions

Graphing piecewise non-linear functions

Frequency distribution and histograms

Reading and drawing bar graphs

read and draw bar graphs

Reading Bar Graphs

Reading and drawing histograms

Reading and drawing line graphs

Reading Line Graphs

Box-and-whisker plots and scatter plots

Bivariate, scatter plots and correlation

Regression analysis

Equation of the best fit line

Stem and leaf plots

The Leaf and Stem of Numbers

Recognizing the Leaf and Stem of Numbers

Recognizing The Leaf And Stem of Numbers Leaf

Recognizing The Leaf And Stem of Numbers Stem

Reading Stem and Leaf Plots — Median

Reading Stem and Leaf Plots — Range

stem and leaf plots Range

Reading Stem and Leaf Plots

Reading Stem and Leaf Plots — Mean

Reading Stem and Leaf Plots — Mode

Frequency polygons

Shapes of distributions

Apprenticeship and Workplace Mathematics 11 (MAT521K)

Measurement

Number

math

- 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? 

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms