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Formula for surface area and volume of cylinders

CA.G.G.C.1

Central angles and proofs

CA.G.G.C.2

Inscribed angles and proofs

CA.G.G.C.3

Circle chord, tangent, and inscribed angles proofs

CA.G.G.C.5

auto-gen

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

Arcs of a circle

Areas and sectors of circles

CA.G.G.CO.1

Central and inscribed angles in circles

Parallel and perpendicular line segments

Identifying Parallel Lines

Identifying Perpendicular Lines

CA.G.G.CO.10

Isosceles and equilateral triangles

CA.G.G.CO.2

Rotational symmetry and transformations

Scale diagrams

Similar polygons

Introduction to transformations

CA.G.G.CO.4

Line symmetry

Perpendicular line proofs

CA.G.G.CO.6

Classifying triangles

Congruence and congruent triangles

CA.G.G.CO.8

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

CA.G.G.CO.9

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

CA.G.G.GMD.1

Circles and circumference

Circle properties

Surface area and volume of cylinders

Surface area and volume of cones

CA.G.G.GMD.3

Surface area and volume of pyramids

Surface area and volume of spheres

CA.G.G.GMD.4

Surface area and volume of prisms

CA.G.G.GPE.1

Conics - Circle

CA.G.G.GPE.2

Conics - Parabola

CA.G.G.GPE.4

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

CA.G.G.GPE.5

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Parallel and perpendicular lines in linear functions

CA.G.G.GPE.6

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>

CA.G.G.MG.3

Word problems of polynomials

CA.G.G.S.CP.1

Organizing outcomes

Calculating Outcomes

CA.G.G.S.CP.2

Probability of independent events

CA.G.G.S.MD.6

Introduction to probability

Identify the Probability — Word Problem

Compound Probability

Reading Probability Models

Probability

CA.G.G.S.MD.7

Comparing experimental and theoretical probability

comparing experimental and theoretical probability

CA.G.G.SRT.1

Enlargements and reductions with scale factors

CA.G.G.SRT.10

Law of sines

Ambiguous case: SSA triangles

Law of cosines

CA.G.G.SRT.11

Applications of the sine law and cosine law

CA.G.G.SRT.2

Similar triangles

CA.G.G.SRT.4

Pythagorean theorem

Pythagorean Theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

CA.G.G.SRT.6

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

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

CA.G.G.SRT.7

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Sum and Difference Identities

Double-angle identities

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

Cofunction identities

CA.G.G.SRT.8

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

CA.G.G.SRT.8.1

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

CA.G.G.SRT.9

Area of triangles: 1/2 a*b sin(C)

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 