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

México

Latinoamérica

Sitemap

Terms of Service

Privacy Policy

Accessibility

Surface Area of a Cylinder: Formula & Example

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

Arithmetic sequences

auto-gen

Arithmetic series

Arithmetic series formula

Geometric sequences

Arithmetic mean vs. Geometric mean

Solve problems that involve SI and imperial units in surface area measurements

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Applications of quadratic 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 SI and imperial units in volume and capacity measurements

Characteristics of quadratic functions

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

Applications of quadratic functions

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

Solve problems that require manipulation and application of formulas related to volume and surface area

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

Completing the square

Completing the Square

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

Demonstrate an understanding of compound interest

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

Geometric series

Geometric Series

Infinite geometric series

Finance: Compound interest

Finance: Compound Interest

Demonstrate an understanding of credit options including credit cards and loans

Solving rational equations

Applications of rational equations

Finance: Future value and present value

Solve problems that require manipulation and application of formulas related to simple interest and finance charges

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

Solve problems that involve creating and interpreting graphs including bar graphs histograms line graphs and circle graphs

Finding the quadratic functions for given parabolas

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of linear inequalities

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

Assignments

Challenge Zone

Foundation Review

Grade 11 Essential Mathematics (30S) - Half Course 3

Develop critical thinking skills

Develop an understanding of spatial relationships applied to volume and surface area

Develop an understanding of credit and the effects of interest

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

The surface area of a cylinder is SA = 2 pi r squared plus 2 pi r h, the two circular bases plus the curved lateral surface, where r is the radius and h is the height. Learn where the formula comes from by unrolling the cylinder, the volume formula, lateral surface area, and a worked example.

Unlock Full Access

Topic Progress

Pug Score

Overview

Surface Area of a Cylinder

What You'll Learn

Surface area of a cylinder: SA = 2 pi r squared + 2 pi r h (two circles plus the curved side).

Unrolled, the curved side becomes a rectangle with width equal to the circumference.

Volume of a cylinder: V = pi r squared times h.

Lateral surface area (curved side only, no circles) is 2 pi r h.

A cylinder's volume has no one-third factor since its cross-section is constant.

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