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Formula for surface area and volume of cylinders

Derive proofs involving properties of angles and triangles

Classifying triangles

Isosceles and equilateral triangles

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Solve problems involving properties of angles and triangles

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Unit circle

Angles in a circle

Determining non-permissible values for trig expressions

Solve problems involving cosine law and sine law, including ambiguous case

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Analyze and prove conjectures using inductive and deductive reasoning to solve problems

Null hypothesis and alternative hypothesis

Proving claims

Confidence levels, significance levels and critical values

Test statistics

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

Line symmetry

Rotational symmetry and transformations

Solve problems involving application of rates

Direct variation

Identifying direct variations

Rate of change

Applications of linear relations

Solve problems involving scale diagrams using proportional reasoning

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Understand relationships among scale factors, areas, surface areas, and volumes of similar 2-D shapes and 3-D 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

Model and solve problems involving systems of linear inequalities in two variables

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Inequalities of combined functions

Inequalities of Combined Functions

Graphing systems of linear inequalities

Applications of inequalities

Demonstrate understanding of characteristics of quadratic functions

Characteristics of quadratic functions

Transformations of quadratic functions

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

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

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Operations of Functions – In a Nutshell

Inverse functions

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

Demonstrate understanding of normal distribution, including standard deviation and z-scores

Introduction to normal distribution

The Normal Distribution and the 68-95-99.7 Rule

Using "invNorm" to Solve Normal Distribution Problems

Normal distribution and continuous random variable

Z-scores and random continuous variables

Interpret statistical data using confidence intervals, confidence levels, and margin of error

Point estimates

Confidence levels and critical values

Margin of error

Margin of Error

Making a confidence interval

Confidence intervals to estimate population mean

Critically analyze society's use of inferential statistics

Traditional hypothesis testing

Traditional Mean Hypothesis Testing

P-value hypothesis testing

Proportion Hypothesis Testing

Mean hypothesis testing with t-distribution

Hypothesis Testing Mean Claims without Knowing <katex> \sigma </katex>

Mathematics 11

Logical Reasoning

Measurement

Relations and Functions

math

Ex. 1:

Hi. Welcome to this Question Here. Okay, the question asks for the surface area and the volume of a cylinder, which is good because we do have a nice equation for these questions here. So to start off, we're going the diameter equals to 42 feet and the height is 110 feet. The units are being consistent, which is good. But we don't really use diameter that much when it comes to the equation, so we're going to change them to radius. Okay? So it's a quick calculation. Just take the 42 and divide it by 2 and you get yourself the radius to be to equal to, I'm just going to put it on the side here, to be 21 feet, 21 feet right there. So let's start off by calculating the surface area first, okay? 
So surface area. Now, the equation says its 2 pi r-squared, and plus the 2 pi r with the h. Now, some people might be wondering, so why is it the equation looks like this is? Is there any reason for this to occur? It's straightforward. If you actually unwrap the cylinder, you will see that it's a circle on the top with a rectangular shape in the middle and followed by another circle. Okay? So if you unwrap it open, that's what you see. We&apos;ve got two circles and the one rectangles. That 2 pi r-squared -- the pi r-squared is the area of the circle, and since there are two of them, that's why we&apos;ve got the two here. The 2 pi r over here is the circumference of the circle, because when you unwrapped it, the length of the rectangle over here is the circumference. That's where the 2 pi r comes in. And the height is just this guy right here. Okay? 
So that's where you get the equation from. So the rest of the work to find the surface area, just plug it in. So here we go really quickly, we&apos;ve got 2 pi times the radius. That's why we had to find the radius first. We're going to square that, plus the 2 pi times the radius, 21 times the height is 110. And just use your calculator. Punch it in. You should get the answer. It turns out to be 17285 and we&apos;ve got feet, and it's a square. Okay? 
Quickly, let's do the next part, which is the volume. The volume of the cylinder is also called with the equation itself. It's just the area of the base times the height. So we're going to put down the base area, and we're going to say times the height, just like that. Now, if you look at the diagram of the cylinder, the base is the circular part, which is the bottom, right here. Okay? Or on the top, this piece right here. Identical piece. So it's a circle. Therefore the area of the circle is going to be a pi r-squared, and the height is given on the side, 110. So let's quickly fill in the information that we have. Here's my pi. The radius is 21 squared, and times the h, 110, and your answer now would be 152398.7 and we&apos;ve got ourselves the feet cubed. Remember that volume's are in cubes, the surface area are in squares. Okay? And that's your answer, right here. Thanks for watching.

A cylinder is like stacking up a pile of circle plates. With information such as, height, <a href='[[glossary.html|{"keyword":"Radius of a Circle or Sphere"}]]'>radius</a>, and circumference, it is easy to calculate the surface area and volume of cylinders.Let's look at how to calculate the surface area and volume of composite solids too.

Surface area of cylinders

Volume of cylinders

Circles and circumference 

Arcs of a circle