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## The Amazing World of 3-D

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Presentation Transcript

The purpose of this slideshow is to:

- reinforce the topics covered in class including 3-D figures, volumes, and surface areas
- Help you to practice some word problems before the upcoming test

Click to Continue

After this slide show you should be able to:

- identify the major characteristics of a cylinder, cone, pyramid, and sphere
- Using the formulas for the volume and surface area of each figure, solve some real world problems involving 3-D figures

Click to Continue

Suppose you have a new bedroom and need to paint your room a new bright red instead of the old yellow paint. How do you know how much paint to buy when you go to the store??

Amazingly the answer is found in GEOMETRY!!

Click to Continue

Careers that involve Geometry:

- Architecture
- Video Game Programmer
- Computer Aided Design
- Software Engineer
- Astronomer
- Robotics

…and many, many more!

Click HERE to Continue

Click on the following buttons to :

Go to the next slide

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Go to the previous slide viewed

Go to the table of contents

2-D vs. 3-D objects

Learn about 3-D Figures

Volume and Surface Area

Cube

Sphere

Cylinder

Cone

Pyramid

Quiz

- 2-Dimensional objects have length and width, but NOdepth

- 3-Dimensional objects have length, width, ANDdepth

- In this lesson we will be focusing on 3-Dimensional objects

To learn about 3-D objects and figures

Click Here

First we need to understand some terms:

Volume: the amount of space occupied by a 3-D figure or region of space

Example: how much milk is poured into a glass

Surface Area:the total area of all the faces of a 3- Dimensional figure

Example: how much leather is used to create a soccer ball

- Now that you know what volume and surface area are, it’s time to learn about some 3-D figures!

To learn about Cubes

Click Here!

A Cube is a 3-Dimensional Figure having six matching sides

Volume: V = L3

Volume = (length of one of it’s sides)3

= (L x L x L)

Surface Area: S = 6 ( L x L)

Surface Area = 6 times the area of one of it’s sides

What is the surface area?

Practice:

An ice cube has 6 equal sides and the length of one of its sides is 4 cm

* Try each problem on scrap paper, then click to reveal the answer when you are ready

What is the volume of the ice cube?

Given: L = 4 cm

Remember: V = L3

Answer:

Click Answer to reveal answer

What is the surface area of the ice cube?

Given: L = 4 cm

Remember: S = 6(L x L)

Answer:

Click Answer to reveal answer

What is the surface area of the ice cube?

Given: L = 4 cm

Remember: S = 6(L x L)

Answer:

S = 6(4 cm x 4 cm)

S = 6(16 cm2)

Surface Area = 96 cm2

You should now have a good understanding of:

- The major characteristics of a cube
- How to calculate the volume and surface area of a cube

To learn about spheres

Click Here!

A Sphere is a 3-Dimensional Figure with all of it’s points the same distance from it’s center point

Volume: V = 4/3 x p x r3

Volume = 4/3 x pi x (radius)3

* where r is the radius of the sphere *

Surface Area: S = 4 x p x r2

Surface Area = 4 x pi x (radius)2

What is the surface area?

Practice:

You just bought a brand new volleyball and it has a radius of 0.4 ft

* Try each problem on scrap paper, then click to reveal the answer when you are ready

What is the volume of the volleyball?

Given: r = 0.4 ft

Remember: V = 4/3 x p x r3

Answer:

Click Answer to reveal answer

What is the volume of the volleyball?

Given: r = 0.4 ft

Remember: V = 4/3 x p x r3

Answer:

V = 4/3 x p x (0.4 ft)3

V = 4/3 x p x (0.064 ft3)

Volume = 0.268 ft3

What is the surface area of the volleyball?

Given: r = 0.4 ft

Remember: S = 4 x p x r2

Answer:

Click Answer to reveal answer

What is the surface area of the volleyball?

Given: r = 0.4 ft

Remember: S = 4 x p x r2

Answer:

S = 4 x p x (0.4 ft)2

S = 4 x p x (0.16 ft2)

Surface Area = 2.01 ft3

You should now have a good understanding of:

- The major characteristics of a sphere
- How to calculate the volume and surface area of a sphere

To learn about cylinders

Click Here!

A Cylinder is a 3-Dimensional Figure having two equal circular bases that are parallel

Volume: V = h x p x r2

Volume = height x pi x (radius)2

* where h is the height of the cylinder *

Surface Area: S = 2prh + 2pr2

Surface Area = (2 x p x r x h) + (2 x p x r2)

What is the surface area?

Practice:

A can of your favorite pop has a height of 4 in. and the radius of one of the bases is 3 in.

* Try each problem on scrap paper, then click to reveal the answer when you are ready

What is the volume of the pop can?

Given: radius of base = 3 in

height of cylinder = 4 in

Remember: V = h x p x r2

Answer:

Click Answer to reveal answer

What is the volume of the pop can?

Given: radius of base = 3 in

height of cylinder = 4 in

Remember: V = h x p x r2

Answer:

V = 4 in x p x (3 in)2

V = 4 in x p x 9 in2

Volume = 113.1 in3

What is the surface area of the pop can?

Given: r = 3 in

h = 4 in

Remember: S = 2prh + 2pr2

Answer:

Click Answer to reveal answer

What is the surface area of the pop can?

Given: r = 3 in

h = 4 in

Remember: S = 2prh + 2pr2

Answer:

S = 2p(3in)(4in) + 2p(3 in)2

S = 2p(12 in2) + 2p(9 in2)

Surface Area = 131.9 in2

You should now have a good understanding of:

- The major characteristics of a cylinder
- How to calculate the volume and surface area of a cylinder

To learn about cones

ClickHere!

A Cone is a 3-Dimensional Figure having a circular base and a single vertex

Volume: V = 1/3 x p x r2 x h

Volume = 1/3 x pi x (radius)2 xheight

where h is the height of the cone

*

*

and r is the radius of the base of the cone

While driving for a Drivers Ed course you hit a cone marking a pothole. The height of the cone is 1 yd and the radius of the base is 0.25 yd

What is the volume?

* Try each problem on scrap paper, then click to reveal the answer when you are ready

What is the volume of the cone?

Given: radius of base = 0.25 yd

height of cone = 1 yd

Remember: V = 1/3 x p x r2 xh

Answer:

Click Answer to reveal answer

What is the volume of the cone?

Given: radius of base = 0.25 yd

height of cone = 1 yd

Remember: V = 1/3 x p x r2 xh

Answer:

V = 1/3 x p x (0.25 yd)2 x 1yd

V = 1/3 x p x 0.0625 yd2 x 1yd

Volume = 0.065 yd3

You should now have a good understanding of:

- The major characteristics of a cone
- How to calculate the volume of a cone

To learn about pyramids

ClickHere!

A Pyramid is a 3-Dimensional Figure with a squarebase and 4triangle-shapedsides

Volume: V = 1/3 x B x h

Volume = 1/3 x area of the base xheight

where h is the height of the pyramid

*

*

and B is the area of the base of the pyramid

You decide to take a trip to Egypt and you visit the Great Pyramid of Giza. You learn that the height of the pyramid is 450 ft and the length and width of the base are both equal to 755 ft

What is the volume?

* Try each problem on scrap paper, then click to reveal the answer when you are ready

What is the volume of the pyramid?

Given: l and w of base = 755 ft

h = 450 ft

Remember: V = 1/3 x B x h

Answer:

Click Answer to reveal answer

What is the volume of the pyramid?

Given: l and w of base = 755 ft

h = 450 ft

Remember: V = 1/3 x B x h

Answer:

V = 1/3 x(755 ft x 755 ft) x 450 ft

V = 1/3 x(570,025 ft2) x 450 ft

Volume = 256,511,250 ft3

You should now have a good understanding of:

- The major characteristics of a pyramid
- How to calculate the volume of a pyramid

To continue to the Quiz

ClickHere!

Now try some problems on your own!

- Do each problem on scrap paper and then click to reveal the answer when you are ready
- Keep track of how many problems you get right/wrong
- Click the button if you need the formulas and the button to return to the problem

A can of soup has a height of 6 in and the radius of the circular base is 2.3 in

How much soup does the can have in it?

TRY IT!

How much soup does the can have in it?

Click HERE to reveal the answer

How much soup does the can have in it?

Click HERE to reveal the answer

If you calculated 99.7 in3 of soup…

You Are CORRECT!

That’s a lot of soup!

If a label needed to go around the entire same can of soup, including the top and bottom base, how big would the label be?

TRY IT!

Click HERE to reveal the answer

Click HERE to reveal the answer

If you calculated 213.9 in2 for the label…

GREAT JOB!

A pyramid fortress is being built at the beach with sand. The height of the pyramid is 3.2 ft. The width of the base is 2.1 ft and the length of the base is 2.1 ft

How much sand was used?

TRY IT!

How much sand was used to build the pyramid?

Click HERE to reveal the answer

How much sand was used to build the pyramid?

Click HERE to reveal the answer

If you calculated 2.24 ft3 of sand…

That’s INCREDIBLE!

A birthday present your giving to your best friend has six even sides with length of 1yd. The present needs to be wrapped…

How much wrapping paper should be used to completely cover the present, no more, no less?

TRY IT!

How much wrapping paper is needed to just cover the present?

Click HERE to reveal the answer

How much wrapping paper is needed to just cover the present?

Click HERE to reveal the answer

If you calculated 6 yd3 of wrapping paper…

STUPENDOUS!

Shelly has eaten the ice cream in her cone so that the ice cream is filled only up to the base of the cone.

How much ice cream is left in the cone if the radius of the cone is 3.2 cm and its height is 11.5 cm?

TRY IT!

How much ice cream is in the cone?

Click HERE to reveal the answer

How much ice cream is in the cone?

Click HERE to reveal the answer

If you calculated 123.3 cm3 of ice cream…

Fantastic!

A cylinder shaped glass with a height of 5.1 in is filled with milk to eat with cookies. The diameter of the base of the glass is 1.4 in and the height of the milk in the glass is 2.8 in

How much milk is in the glass?

TRY IT!

How much milk is in the glass?

Hint: ½ of diameter = radius

Click HERE to reveal the answer

If you calculated 4.31 in3 of milk…

Congratulations!

How much of the glass is not filled with milk?

Click HERE to reveal the answer

Click HERE to go back to the problem

How much of the glass is not filled with milk?

Click HERE to reveal the answer

Click HERE to go back to the problem

If you calculated 3.54 in3 of glass…

You Are Correct!

A brand new basketball has a radius of 0.5 ft across the center of the ball

How much air does the ball hold?

TRY IT!

How much air does the ball hold?

Click HERE to reveal the answer

How much air does the ball hold?

Click HERE to reveal the answer

If you calculated 0.52 ft3 of air…

AWESOME!

How much leather would be needed to cover the surface of the ball?

Click HERE to reveal the answer

How much leather would be needed to cover the surface of the ball?

Click HERE to reveal the answer

If you calculated 3.14 ft2 of leather…

Amazing!

A unique swimming pool with six even sides of length 15 m is being filled with water

How much water can the pool hold before it overflows?

TRY IT!

How much water can the pool hold before it overflows?

Click HERE to reveal the answer

How much water can the pool hold before it overflows?

Click HERE to reveal the answer

If you calculated 3,375 m3 of water…

You’re Right!

- If you got 7 or more correct on the first try click HERE

- If you got less than 7 correct on the first try click HERE

You now have a good understanding of how to calculate the

VOLUME and SURFACE AREA of a:

- Cone

- Cube

- Pyramid

- Cylinder

- Sphere

If you would like to go back and review any topics, click

- For further references, information, and games about geometry, click any of the following links:

Geometry in Action

Geometry in Real World: Students as Architects

Geometry Games

GREAT JOB!

You may need to go back and review some topics and/or examples

Click and choose a topic to review and then try the quiz again

GOOD LUCK!

Volume

Surface Area

Cube: V = L3

Cube: S = 6L2

Sphere: S = 4pr2

Sphere: V = 4/3pr2

Cylinder:

Cylinder: V = hpr2

S = 2prh + 2pr2

Cone: V = 1/3pr2h

Pyramid: V = 1/3Bh

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