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Understanding surface area of 3D shapes

TX.G.10.A

Surface area of 3-dimensional shapes

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

TX.G.10.B

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Upper and lower bound

Upper and Lower Bound

TX.G.11.B

Areas and sectors of circles

TX.G.11.C

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

TX.G.11.D

Introduction to volume

Calculate the Volume

TX.G.12.A

Angles in a circle

Chord properties

Tangent properties

Circles and circumference

Circle properties

Central angles and proofs

Inscribed angles and proofs

Central and inscribed angles in circles

TX.G.12.B

Arcs of a circle

Circle chord, tangent, and inscribed angles proofs

TX.G.12.D

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

TX.G.12.E

Conics - Circle

TX.G.13.A

Permutations

Combinations

Problems involving both permutations and combinations

TX.G.13.B

Probability

TX.G.13.C

Probability of independent events

Addition rule for 

Addition Rule for "OR"

Addition rule for "OR"

Multiplication rule for 

Multiplication rule for "AND"

Multiplication Rule for "AND"

TX.G.13.D

Conditional probability

Probability with Venn diagrams

TX.G.13.E

Determining probabilities using tree diagrams and tables

Probability involving permutations and combinations

TX.G.2.A

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>

TX.G.2.B

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>

Parallel and perpendicular lines in linear functions

TX.G.2.C

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

TX.G.3.A

Rotational symmetry and transformations

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

TX.G.3.B

Combining transformations of functions

Enlargements and reductions with scale factors

TX.G.3.C

Scale diagrams

TX.G.3.D

Line symmetry

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

TX.G.4.A

Inductive reasoning

Deductive reasoning

TX.G.4.B

Conditionals

Inverses, converses, and contrapositives

Biconditionals

TX.G.4.D

Algebraic proofs

TX.G.5.A

Congruence and congruent triangles

Pairs of lines and angles

Parallel lines and transversals

Perpendicular line proofs

TX.G.5.D

Classifying triangles

TX.G.6.A

Isosceles and equilateral triangles

Parallel line proofs

TX.G.6.B

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

TX.G.6.D

Combination of SohCahToa questions

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

TX.G.6.E

Classifying quadrilaterals

Classifying Quadrilaterals

Word Problem: Classifying Quadrilaterals

TX.G.7.A

Similar triangles

Similar polygons

TX.G.8.B

Estimating square roots

TX.G.9.A

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

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

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

TX.G.9.B

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Circles

Coordinate and transformational geometry

Logical argument and constructions

Proof and congruence

Two-dimensional and three-dimensional figures

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