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Master Surface Area of Cylinders: Formulas & Examples

MA.912.GR.1.1

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

MA.912.GR.1.2

Classifying triangles

Congruence and congruent triangles

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

MA.912.GR.1.3

Isosceles and equilateral triangles

MA.912.GR.1.6

Similar triangles

Similar polygons

MA.912.GR.2.1

Rotational symmetry and transformations

MA.912.GR.2.2

Enlargements and reductions with scale factors

MA.912.GR.2.3

Scale diagrams

MA.912.GR.2.5

Introduction to transformations

Horizontal and vertical distances

MA.912.GR.2.6

Draw on coordinate planes

MA.912.GR.2.8

Cartesian plane

Cartesian Plane — Coordinates

MA.912.GR.3.1

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Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

MA.912.GR.3.2

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

MA.912.GR.3.3

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

MA.912.GR.4.1

Surface area of 3-dimensional shapes

MA.912.GR.4.2

Line symmetry

MA.912.GR.4.3

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

MA.912.GR.4.5

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

MA.912.GR.4.6

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

MA.912.GR.5.1

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

MA.912.GR.5.2

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

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

MA.912.GR.5.3

Circles and circumference

Circle properties

MA.912.GR.6.1

Arcs of a circle

MA.912.GR.6.2

Areas and sectors of circles

Central angles and proofs

Inscribed angles and proofs

MA.912.GR.6.3

Central and inscribed angles in circles

Circle chord, tangent, and inscribed angles proofs

MA.912.GR.6.4

Angles in a circle

Chord properties

Tangent properties

MA.912.GR.7.2

Conics - Circle

MA.912.GR.7.3

Conics - Parabola

Conics - Ellipse

Conics - Hyperbola

MA.912.LT.4.10

Biconditionals

Deductive reasoning

Algebraic proofs

MA.912.LT.4.3

Inductive reasoning

Statements

Negations

Conjunctions and disjunctions

Truth tables

Conditionals

Inverses, converses, and contrapositives

MA.912.T.1.1

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

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

Combination of SohCahToa questions

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

MA.912.T.1.2

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Pythagorean theorem

Pythagorean Theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

math

Intro

<p>- Hi, welcome to this question right here. So we're going to find the surface area of the cylinder. Now there is an equation for this because what happened is if you unwrap the cylinder open, technically it looks like you have a circle on the top and followed by a rectangular piece in the middle. Another circle at the end. Because that's the top, bottom and that's the middle piece. So the equation for the surface area for your cylinder is actually the pi R square, this part here refers to the area of the circles. This one right here, but we have two identical circles here. So you just need to a two in the front. So the two pi R square will give you the area of the circles here and here. Now what about the one in the middle? The one in the middle, you add on top of that. The one in the middle happens to be a rectangle. Now we already know the height here is seven, because that is the height right there. So it's just going to be the height but it's going to multiply this side right here which is the length, but where's the length? Imagine if you wrap it around the circle, that wrapping around the circle is actually the circumference. So the length over here, I'll write that down, is actually just the circumference which is the C, and C equals to, the two pi R okay? So at the end, we're not taking the length times the width. It's actually the two pi R times the width. So I'm going to put down the two pi R right here, and I'm just going to times the height in this equation here. So literally this is the equation to calculate the surface area of any cylinder. Okay?<br />
So there you go. We're going to plug the numbers in. I got the two times the pi, times the radius. I was given the radius, it was three centimeters. I got to square that, plus the two pi times this three, and times the height which is seven. All you have to do is grab your calculator and just punch everything inside. We're going to get some decimals, but it's fine. Two times pi. So we have two times pi and times three squared, and plus two times the pi, times this three times 21, okay? Now we have 60 pi, okay? If you're looking for like the exact value of answers, this is the final answer for your-- like the exact numbers which is 60 pi, okay? But if you don't want it, you want some decimals, then it's going to get you the 188.50 centimeter square, and this is your final answer for this question. Thanks for watching.</p>


As long as we have the diameter or <a href='[[glossary.html|{"keyword":"Radius of a Circle or Sphere"}]]'>radius</a> and the height of the cylinder, we are able to find its surface area in no time. The surface area of a cylinder is basically adding the surface are of a rectangle and two circles together. The most difficult part is to find the circumference of the circles, which is also one of the sides of the rectangle.

How to find the surface area of cylinders

Circles and circumference 