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Master Surface Area of Cylinders: Formulas & Examples

Geometry: Master Shapes, Proofs & Spatial Reasoning

Angles and Lines

Angle relationships

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Parallel and perpendicular line segments

Identifying Parallel Lines

Identifying Perpendicular Lines

Perpendicular bisectors

Angle bisectors

Angle Bisectors

Coordinate Plane

Cartesian plane

Cartesian Plane — Coordinates

Draw on coordinate planes

Triangles

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Classifying Triangles

Isosceles and Equilateral Triangles

Circles

Angles in a circle

Chord properties 

Tangent properties

Circles and circumference 

Circle properties

Arcs of a circle

Areas and sectors of circles

Central angles and proofs

Inscribed angles and proofs

Central and inscribed angles in circles

Circle chord, tangent, and inscribed angles proofs

Surface Area and Volume

Volume of rectangular prisms word problems

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Introduction to volume

Calculate the Volume

Volume of prisms

Find the volume

Volume of Prisms Calculate Area and Volume

Rectangular Prisms Table

Volume of Prisms — Word Problem

Volume of cylinders

Word problems relating volume of prisms and cylinders

Surface area of cylinders

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

Transformations

Identifying vertices

Line symmetry

Rotational symmetry and transformations

Understanding tessellations

understand tessellations Interior Angle

Tessellations using translations and reflections

tessellations using translations and reflections

Tessellations using rotations

Introduction to transformations

Horizontal and vertical distances

Similarity

Similar solids

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Congruence

Congruence and congruent triangles

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

Logic

Inductive reasoning

Statements

Negations

Conjunctions and disjunctions

Truth tables

Conditionals

Inverses, converses, and contrapositives

Biconditionals

Deductive reasoning

Algebraic proofs

Reasoning

Consecutive integers

Number sequences

Finding the missing digit

math

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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