About Us

Why Choose StudyPug

How it works

Pricing

Testimonials

Contact Us

Blog

Basic Math

Algebra

Geometry

Trigonometry

Calculus

Linear Algebra

Differential Equations

Statistics

Chemistry

Organic Chemistry

Physics

Microeconomics

For Students

For Parents

For Home Schoolers

For Teachers

Australia

Canada

Ireland

New Zealand

Singapore

United Kingdom

United States

Sitemap

Terms of Service

Privacy Policy

Master Surface Area and Volume of Prisms: Key Geometry Skills

Grade 11 Math: Master Advanced Concepts & Skills

Forms of mathematical reasoning

auto-gen

Set notation

Understanding How to Use Set Notation

Set builder notation

Intersection and union of 2 sets

Intersection and Union of 2 Sets

Intersection and union of 3 sets

Intersection and Union of 3 Sets

Angle relationships

Unit circle

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Use tangent ratio to calculate angles and sides (Tan = o / a)

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

Classifying triangles

Isosceles and equilateral triangles

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Graphical analysis

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Inverse functions

Operations with functions

Quadratic function in vertex form: y = a(x-p)^2 + q

Applications of inequalities

Optimization - inequalities

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

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

Inequalities of combined functions

Inequalities of Combined Functions

Applications of statistics

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Solving polynomial inequalities

Completing the square

Completing the Square

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Frequency distribution and histograms

Center of a data set: mean, median, mode

Spread of a data set - standard deviation & variance

Measures of relative standing - z-score, quartiles, percentiles

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

Census and bias

Census and Bias

Classifying Bias

Scale models

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

Solving 3 variable systems of equations (no solution, infinite solutions)

System of Equations With No Solution

System of Equations With Infinite Solutions

System of Equations With Infinite Solutions - Extended

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Financial literacy

Finance: Compound interest

Finance: Compound Interest

Finance: Future value and present value

Similar shapes and objects

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

Optimization

Logical reasoning

Addition rule for 

Addition Rule for "OR"

Addition rule for "OR"

Multiplication rule for 

Multiplication rule for "AND"

Multiplication Rule for "AND"

Conditional probability

Probability involving permutations and combinations

Variation in statistical analysis

Bivariate, scatter plots and correlation

Regression analysis

Equation of the best fit line

Aligned with your class and textbook, our comprehensive Grade 11 math help covers all topics that you would expect in any typical grade 11 math classes, whether it&apos;s <a href="http://www.edu.gov.on.ca/eng/curriculum/secondary/grade11.html">Ontario math curriculum</a>, <a href="https://curriculum.gov.bc.ca/curriculum/10-12#m">B.C.</a>, <a href="https://education.alberta.ca/mathematics-10-12/programs-of-study/">Alberta</a>, <a href="http://www.edu.gov.mb.ca/k12/cur/math/framework_9-12/index.html">Manitoba</a>, <a href="https://www.curriculum.gov.sk.ca/webapps/moe-curriculum-BBLEARN/index.jsp?lang=en&subj=mathematics&level=precalc20">Saskatchewan</a>, <a href="http://www.ed.gov.nl.ca/edu/k12/curriculum/guides/mathematics/">Newfoundland</a>, or other provinces.

Our video lessons walk you through all topics in trigonometry like Unit circle, Factoring trinomials, Radicals, Rational expressions, Quadratic equations, Sequences and series, and so many more. Learn the concepts with our tutorials that show you step-by-step solutions to even the hardest math problems. Then, reinforce your understanding with tons of grade 11 math practice.

All our lessons are taught by experienced Grade 11 Math teachers. Let&apos;s finish your homework in no time, and ACE that final.

Foundations of Mathematics 11

math

<h2>Is grade 11 math hard?</h2>
Grade 11 math can be a struggle and will definitely put your math skills to the test. This can make it seem like grade 11 math is hard and overwhelming. But fear not &ndash; here at StudyPug we&apos;ve made sure to address all your questions and concerns! From topics such as quadratic functions to Sigma notation, down to unraveling the Vertex formula, (and even more!) we&apos;re here to provide you help with grade 11 math. Our carefully crafted Grade 11 math tutorials are well suited for all &ndash; so whether you are a student that requires a refresher on fundamentals or a keener looking to get ahead of the game, we have content covering Grade 11 math for dummies as well as more advanced, challenging content. Regardless of the level of difficulty, we&apos;re here to help you every step of the way with step-by-step examples and lots of practice questions. Grade 11 Math does not have to be hard folks! With help from our review lessons and methodical-disciplined practice, you&apos;ll find yourself powering through the difficult questions with ease and confidence in no time!

<h2>How to prepare for grade 11 math?</h2>
Feeling unprepared for another year of math? Unsure about how and where to get started with grade 11 math? StudyPug has all the tools and resources for you to get you prepared and equipped for grade 11 math!
Understanding grade 11 math will take time and that can be difficult if you only see your tutor once a week or feel like you need a refresher on topics previously covered in class. Here at StudyPug our Grade 11 math tutors and all of our content are readily at your disposal whenever you need them. With 24/7 help and 1000&apos;s of lessons at your fingertips, we are here to help you exercise your understanding of grade 11 math topics and prepare for your upcoming Grade 11 math test and/or Grade 11 math exam preparation. Still feeling like you need more support and background information on some of the topics covered in grade 11 math? Some of the topics you are learning in Grade 11 math (e.g. Quadratic relations, completing the square) we started introducing in <a href='[[region_textbook.html|{"textbook_key":"grade10"}]]'>Grade 10 math</a>. <a href='[[region_textbook.html|{"textbook_key":"grade10"}]]'>Grade 10 math</a> is a prerequisite course for Grade 11 math and we strongly recommend a strong command of the knowledge and skills learned in Grade 10 to help you succeed in Grade 11 math. Head over to our <a href='[[region_textbook.html|{"textbook_key":"grade10"}]]'>Grade 10 math page</a> to begin your revision now!

<h2>How do I use StudyPug to study Grade 11 Math?</h2>
Our intention for StudyPug was to create a 24/7, online companion to meet all your Grade 11 math tutoring needs. We&apos;ve carefully designed our website to be intuitive and easy to navigate but we&apos;ve also included this section for those of you that are visiting or trying us out for the first time. Keep in mind that if you are a student that is still unsure about whether StudyPug is for you, you can still sample our product/service by beginning with the free lessons that are accessible immediately without hassle.
As a general guideline, before jumping into any of our topics in grade 11 math, we recommend starting with assessing your prior knowledge. This is simply done by reviewing your familiarity with concepts we believe you should have a relatively strong command of. Almost all of our topics begin with an outline on the basic concepts you should know as well as other related, pertinent concepts.
If you know exactly what you are looking for, we recommend jumping straight to using our search engine tool. Use this to hone in on the concepts, topics, or questions you are finding the most difficult. Remember; don&apos;t be afraid if you feel like you need to begin with some of the rudimentary foundations you covered previously in grade 10 math or elsewhere.
Once you have identified the topic you require more work on, our short but informative video lessons wills walk you through examples (from easy to complex problems) to flesh out the concepts you need to learn as well as study tips and strategies. Watch and re-watch these lessons as many times as you need! We also provide a paraphrased transcript on the gist of what was addressed in the video if you prefer to learn and revise this way instead.
Last but certainly not the least of these steps, we encourage you to put your knowledge and skills to the test! We&apos;ve prepared plenty of questions per topic for you to master and perfect! See how well you have learnt and acquire more practice from a wide variety and range (i.e. easy to hard) of questions.
Looking for a more entertaining read and method to learn some grade 11 math? <a href="https://www.studypug.com/blog/beauty-and-the-beast/">Swing by our blog to learn about the fibonacci sequence and Kim Kardashian!</a>

<h2>How to pass 11th grade math?</h2>
Preparing for a grade 11 Math test or exam? You&apos;ve come to right place! Our home page <a href='[[region_textbook.html|{"textbook_key":"grade11"}]]'>https://www.studypug.com/ca/grade11</a> has everything you need to learn Grade 11 Math. Here at StudyPug we exist to help you achieve your academic goals. So whether you are gearing up for a chapter test on the unit circle or require a quick overview of several topics for your big final exam, we want to make sure you are feeling confident in tackling all your assessments.
At StudyPug we provide numerous Grade 11 math lessons spanning multiple provincial, and international curriculums. We also build content around several renowned textbooks, so we&apos;re well on our way to helping you focus on the numerous topics and types of questions you may be struggling with in 11th grade math.
Remember this &ndash; learning and preparing to pass 11th grade math will not happen overnight! So do not fret if you are finding certain chapters or problems more challenging than others. The key is to first ensure a strong grasp of the underlying concepts and then get into the habit of exercising your knowledge through practice. With over 290 unique practice questions in total for 11th grade math, we readily supplement your classroom learning with the objective of not to merely pass 11th grade math, but to also obtain excellent grades while in the process. Our inventory of practice questions is available to you immediately and should make easy practice out of 11th grade math questions.

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-grade11math.png

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

Surface area of prisms

Volume of prisms