1. Applications of Three-Dimensional Geometry

2. Cans and Jars are cylinders

3. Boxes and Bricks are prisms

4. Basketballs and oranges are spheres

5. Prisms
Geometric figures that have two congruent bases that are connected by the lateral faces that are parallelograms.

6. Surface Area of a Prism We open it up like a cardboard box.
Then, we find the areas of all the geometric figures.

7. SA of Cylinders
A cylinder is a tube and is composed of two parallel congruent circles and a rectangle which base is the circumference of the circle.

8. Surface Area of a cylinder
Note: B is not the same as b, (as in A = 1 2 bh )

9. The area of one circle is:
The circumference of a circle:
C=πd
C=π⋅4
C≈12.6
The area of the rectangle:
A=C⋅h
A=12.6⋅6
A≈75.6
The surface area of the whole cylinder:
A= =100.8units2

10. Surface Area of Rectangular and triangular prisms SA= ph +2B

11. To find the volume of a prism (it doesn't matter if it is rectangular or triangular) we multiply the area of the base, called the base area B, by the height h.
V=B⋅h

12. Volume of a cylinder and A Prism

13. Surface Area
If you want to paint a house, make a car cover, or find the material needed to make a hollow shape, you will need to know surface area.
For simple shapes, you can find the surface area of the sides and add them together.
For a sphere, you multiply the area of the circle inside the sphere times 4.
SA= 4𝜋𝑟2
video

14. John has a 3D printer, and he plans to print 16 hollow balls for a mobile he’s designing. Each ball will have a three-inch diameter. He needs to know how much material he will need for this project.
Understand: What do you want/need to know?

15. John has a 3D printer, and he plans to print 16 hollow balls for a mobile he’s designing. Each ball will have a three-inch diameter. He needs to know how much material he will need for this project.
Understand: What do you want/need to know?
You need to know the total surface area in square inches.

16. Plan
Write any equations you will need to solve the problem, using formulas for surface area.
SA= 4𝜋𝑟2
SA= 4(3.14)(1.5)2
SA= (12.56)(2.25)
SA= 28.26in2
You will need16 hollow balls, so multiply times 16. = in2

17. Surface Area of a Prism
A pyramid consists of three or four triangular lateral surfaces and a three or four sided surface, respectively, at its base. When we calculate the surface area of the pyramid below we take the sum of the areas of the 4 triangles area and the base square. The height of a triangle within a pyramid is called the slant height.

18. SA of a Prism

19. Surface area of a Cone
The base of a cone is a circle and that is easy to see. The lateral surface of a cone is a parallelogram with a base that is half the circumference of the cone and with the slant height as the height. This can be a little bit trickier to see, but if you cut the lateral surface of the cone into sections and lay them next to each other it's easily seen.