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

Formula for surface area and volume of cylinders

Derive proofs that involve the properties of angles and triangles

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Solve problems that involve the properties of angles and triangles

Classifying triangles

Isosceles and equilateral triangles

Solve problems that involve the cosine law and the sine law including the ambiguous case

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

auto-gen

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

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

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

Analyze puzzles and games that involve spatial reasoning using problem-solving strategies

Line symmetry

Rotational symmetry and transformations

Surface area of 3-dimensional shapes

Arithmetic mean vs. Geometric mean

Solve problems that involve the application of rates

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

Solve problems that involve scale diagrams using proportional reasoning

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Simplifying complex fractions

Demonstrate understanding of relationships among scale factors areas surface areas and volumes

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

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 that involve systems of linear inequalities in two variables

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Graphing systems of linear inequalities

Applications of inequalities

Demonstrate understanding of characteristics of quadratic functions

Introduction to 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

Completing the square

Completing the Square

Research and give a presentation on a historical event or area of interest that involves mathematics

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

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Geometric sequences

Geometric series

Geometric Series

Infinite geometric series

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

Grade 11 Applied Mathematics (30S)

Develop spatial sense

Develop logical reasoning

Develop spatial sense and proportional reasoning

Develop algebraic and graphical reasoning through the study of relations

Develop an appreciation of the role of mathematics in society

Develop statistical reasoning

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.

Finding surface area and volume of a cylinder given diameter and height

Calculating surface area and volume of a half-cylinder with a rectangular prism

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

Surface area and volume of cylinders

What You'll Learn

Calculate the surface area of cylinders using the formula 2πr² + 2πrh

Find the volume of cylinders by multiplying the base area by height

Convert between diameter and radius to apply cylinder formulas correctly

Determine surface area and volume of composite solids combining cylinders and rectangular prisms

Understand why cylinder formulas work by visualizing the unwrapped shape

What You'll Practice

Finding surface area and volume of complete cylinders given radius and height

Calculating measurements for half-cylinders in composite shapes

Computing total surface area by adding rectangular and cylindrical components

Solving problems with mixed units and converting diameter to radius

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

2 Video lessons

Learning resources

Skills

Surface Area

Volume

Cylinders

Composite Solids

Geometric Formulas

Radius and Diameter

3D Geometry