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Surface Area of 3D Shapes: Formulas for Each Solid

Demonstrate understanding of powers with integral bases and whole number exponents

Using exponents to describe numbers

Expanded powers

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Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Demonstrate understanding of rational numbers by comparing and ordering 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

Explain and apply the order of operations including exponents with and without technology

Order of operations (PEMDAS)

Identify the Order of Operations

Order of Operations — Word Problem

Determine the square root of positive rational numbers that are perfect squares

Determine square roots of rational numbers

Square roots of rational numbers

Squares and square roots

Square Root of a Perfect Square

Determine the approximate square root of positive rational numbers that are non-perfect squares

Estimating square roots

Generalize a pattern arising from a problem-solving context using linear equations

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

Graph linear relations analyze the graph and interpolate or extrapolate to solve problems

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Model and solve problems using linear equations of various forms

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

Solving linear equations with variables on both sides

Solving literal equations

Explain and illustrate strategies to solve single variable linear inequalities

Compound inequalities

Analyze the Alternate Form of Compound Inequalities: AND

Compound linear inequalities

Evaluate Compound Inequalities: And

Express linear inequalities graphically and algebraically

Graph the Inequality

Linear Inequalities – Word Problem 

Linear inequalities

Solving one-step linear inequalities

One-step Linear Inequalities

One-step linear inequalities

One-step Linear Inequalities Decimal

One-step Linear Inequalities Decimal with Fraction

One-step Linear Inequalities Fraction

Solve One Step Linear Inequalities Find Solution– Word Problem

One-step Linear Inequalities — Word Problem

Solving multi-step linear inequalities

Multi-step Linear Inequalities

Two-step Linear Inequalities

Multi-step linear inequalities

Two-step linear inequalities

Solve Multi-step Linear Inequalities – Word Problem 

Solve Multi Step Linear Inequalities Solve Equation – Word Problem

Solve Multi Step Linear Inequalities Equation – Word Problem

Demonstrate an understanding of polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Model record and explain the operations of multiplication and division of polynomial expressions

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

Model and solve problems using linear equations

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

Describe the effect of various factors on the collection of data

Influencing factors in data collection

Data collection

Select and defend the choice of using either a population or a sample of a population

Sampling methods

Sampling Methods

Census and bias

Census and Bias

Classifying Bias

Develop and implement a project plan for the collection display and analysis of data

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Bivariate, scatter plots and correlation

Demonstrate an understanding of the role of probability in society

Probability

Solve problems and justify the solution strategy using circle properties

Angles in a circle

Chord properties

Tangent properties

Determine the surface area of composite 3-D objects to solve problems

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

Demonstrate an understanding of similarity of polygons

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Demonstrate an understanding of line and rotation symmetry

Line symmetry

Rotational symmetry and transformations

Assignments

Challenge Zone

Foundation Review

Grade 9 Math

Develop number sense

Use patterns to describe the world and solve problems

Represent algebraic expressions in multiple ways

Collect display and analyze data to solve problems

Use direct or indirect measurement to solve problems

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.

Finding dimensions and volume of a cut-out corner piece

Finding dimensions of a single block from a rectangular solid

Calculating surface area of a rectangular prism (15×6×6)

Computing the surface area ratio of a block to the full six-block solid

The surface area of a 3D shape is the total area of all its faces and surfaces, measured in square units. Learn the surface area formulas for rectangular prisms, cylinders, cones, and spheres, what each variable means, and how unfolding a solid into a net makes the total easy to find.

Surface Area of 3D Shapes | StudyPug

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Overview

Surface Area of 3D Shapes

What You'll Learn

Surface area is the total area of all faces and surfaces of a solid, in square units.

Rectangular prism: 2 times (lw plus wh plus lh).

Cylinder: 2 pi r squared plus 2 pi r h; sphere: 4 pi r squared.

Unfolding a solid into a net turns surface area into a sum of flat areas.

Surface area measures the outside; volume measures the space inside.

What You'll Practice

Finding dimensions of single blocks from composite rectangular objects

Calculating total surface area by adding areas of all six rectangular faces

Computing surface area ratios between parts and whole objects

Working with multi-step problems involving division and surface area formulas

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

4 Video lessons

Learning resources

Skills

Surface Area

Rectangular Prisms

3D Geometry

Ratios

Spatial Reasoning

Measurement

Problem Solving