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Understanding surface area of 3D shapes

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

<p>- Hi, welcome to this question right here. So this kind of a fun problem, cause right now, you're gonna outline the front, the top, and the left view of this diagram right here. Okay? So, let's do the front first. Okay? Since that was the first one. So, if you look at the front, basically, what we have is, you're looking from this direction. Okay? So, I'm doing the blue ones. So, I got 1, 2, 3, 4, 5, 6. Okay? I got six blocks. If I'm looking from this direction, I have only seen the six blocks. So basically, I got a bottom three. Basically, 1, 2, and 3, it's all there. And I got a top two right here. Okay. So, there's another two and following there is one more on the top. So, that's basically the graph for the front part. Okay? It's good that you havea different color pen, and then you're just gonna dot them and then just visualize and draw just a two-dimensional of the front. Then let's go to the top. Let's change the color of the pen right here. Let's go to the top. Okay? So, doing it from the top, that means you're looking it from the top-down. So, there is your 1, 2, 3, 4, and 5. Okay. So, let's put the dots on that. They're clear but as you can see, there's only two rows if you're looking from the top. And clearly you got the back row all completed. So, I can see it from the back that there is three pieces and then there's two more in the front on the further left right here. So basically, this is what you have from the top view. Okay? Now, let's do it from the side view here. Let's grab the last color right here, which is the red. The side view, pretend that you're looking from this way. Okay? So, there is your 1, 2, and the 3 and there is a 4 on the top. Okay? So, here is my side view right here, let's go to the bottom right there. Here is my side view. I got the first three on the left all completed. Okay? Draw a big one right here and cut it into three equal parts. And then I have one more at the bottom and that's it. Okay? So, that is my side view right here. Again, grab a color pen, pen or pencil, blue pen, black pen, dot them and then you will be able to draw them really easily. Okay? Have fun with them. Thanks for watching.</p>

Imagine you are looking at a 3-dimensional shape, for example, a cereal box. It looks like large rectangle from the front. From the side, it may look like a much thinner rectangle. However, you are sure that it is the same cereal box. It is because 3-dimensional shapes have many surfaces, and they do not necessarily look the same from different angles.

Surface area of three-dimensional (3D) objects