1. Prisms
and
Cylinders

2. Vocabulary…
Lateral Faces
Bases
Base Edges
Lateral edges
Vertices
Lateral Area
Total Surface Area
Volume

3. A prism is named using the name of the base.

4. r2 P P = C = 2πr B h L P x h T L + 2B V B x h Prism Cylinder
(perimeter of the base)
add the sides of polygon
P = C = 2πr B
(area of base)
Area formula for polygon
r2 h
(height of the solid)
Measured from vertex ┴ the middle of the base L
(lateral area)
P x h T
(total surface area)
L + 2B V
(volume)
B x h

5. P = ____ B = ____ h = ____ L = ____ T = ____ V = ____

6. P = ____ B = ____ h = ____ L = ____ T = ____ V = ____

7. P = ____ B = ____ h = ____ L = ____ T = ____ V = ____

8. P = ____ B = ____ h = ____ L = ____ T = ____ V = ____

9. Cube with edge 8 cm.
B = ____ T = ____ V = ____

10. A right triangular prism has lateral area 120 cm2
A right triangular prism has lateral area 120 cm2. If the base edges are 4 cm., 5 cm., and 6 cm. long, find the height of the prism.

11. A cube has a volume of 343 in.3. What is the total surface area of the cube?

12. A cylinder has a total surface area of 27π in. 2 and radius 3 inches
A cylinder has a total surface area of 27π in.2 and radius 3 inches. What is the volume of the cylinder?

13. Homework
Worksheet

14. Warm Up: Find the following
B = _____
L = _____
T = _____
V = _____
2) P = _____
B = _____
L = _____
T = _____
V = _____

15. Pyramids
and
Cones
Surface Area

16. Vocabulary…
Lateral Faces
Base
Base Edges
Lateral edges
Height
Slant height
Apothem of the base
Lateral Area
Total Surface Area

18. Relationships in the pyramid…
Sits OUTSIDE the Pyramid or Cone
Sits INSIDE the Pyramid or Cone

19. L + B 1/3 B x h l ½ Pl V Pyramid Cone (slant height of face) L
(perimeter of the base)
add the sides of polygon
P = C = 2πr B
(area of base)
Area formula for polygon or circle h
(height of the solid)
Measured from vertex  to the middle of the base
(use Pythagorean theorem if not given) l
(slant height of face)
Measure from the vertex  to the midpoint of the base edge (use Pythagorean theorem if not given) L
(lateral area)
½ Pl T
(total surface area)
L + B V
(Volume)
1/3 B x h

20. P = ____ B = ____ h = ____ l = _____ L = ____ T = ____
V = ____

21. P = ____ B = ____ h = ____ l = _____ L = ____ T = ____
V = ____

22. P = ____ B = ____ h = ____ l = _____ L = ____ T = ____
V = ____

23. Find the height of a triangular pyramid with a base area of 130 square meters and a volume of 650 cubic meters.

24. The total surface area of a cone is 27 in2. The radius is 3 in
The total surface area of a cone is 27 in2. The radius is 3 in. What is the slant height?

25. HOMEWORK

26. WARM UP

27. Volume & Surface Area of SPHERES

28. SPHERE:
The set of all points in space equidistant from a given point called the center.
We use the radius of the great circle to find the surface area and volume.

29. FORMULAS V= 4 3 𝜋 𝑟 3 SA =4𝜋 𝑟 2 VOLUME SURFACE AREA Example) Example)
Be careful and note if you’re given diameter or radius!
FORMULAS
VOLUME
SURFACE AREA
V= 4 3 𝜋 𝑟 3
Example)
Radius =
V =
SA =4𝜋 𝑟 2
Example)
Radius =
SA =

30. Example 2
Find the volume and surface area of a sphere with radius = 6 m

31. Example 3
Find the volume and surface area of a sphere with diameter = 8.4 in

32. Example 4
Earth’s equator is about 24, 902 miles long. What is the approximate surface area of the Earth? (Earth’s Equator is a great circle that divides the Earth into two hemispheres)

33. Example 5
The volume of a sphere is 𝑚 3 . What is the surface area rounded to the nearest square meter?

34. Example 6
Find the volume of half of a grapefruit that has a circumference of 14 cm

35. Homework