Name:______________________________________________________ Date: _______________

Geometry 2012-2013

Solid Geometry

Name:______________________________

Teacher:____________________________

Pd: _______

Table of Contents

DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders

Pgs: 1 - 7

HW: Pgs: 8 - 10

DAY 2: SWBAT: Calculate the Volume of Pyramids and Cones

Pgs: 11 - 15

HW: Pgs: 16 - 17

DAY 3: SWBAT: Calculate the Surface Area of Rectangular Prisms and Cylinders

Pgs: 18 - 23

HW: Pgs: 24 - 25

DAY 4: SWBAT: Calculate the Surface Area of “Other” Prisms

Pgs: 26 - 30

HW: Pgs: 31- 32

DAY 5: SWBAT: Calculate the Surface Area of Pyramids and Cones

Pgs: 33 - 37

HW: Pgs: 38- 39

DAY 6: SWBAT: Calculate the Volume and Surface Area of Spheres

Pgs: 40 - 43

HW: Pgs: 44 - 45

Day 7: SWBAT: Calculate the Volume and Surface Area of Three Dimensional Figures (REVIEW) Pgs: 46 - 47

Day 8: SWBAT: Calculate the Volume and Surface Area of Three Dimensional Figures (REVIEW) Pgs: 48 - 51

Summary Page

Pg: 52

Extra Credit

Pg: 53

These formulas are given to you…

These aren’t given to you…but are very useful!

Lateral Area for Prism

L = (Perimeter of the base) (Height of the prism) Or L = Ph

Surface Area for Prisms and Cylinders

S.A. = L + 2B

Lateral Area for Pyramids

L =

(Perimeter of the base) (Slant Height) Or L =

Pl

Surface Area for Pyramids

S.A. = L + B

1

SWBAT: Calculate the volume of prisms and cylinders

Volume of rectangular solids and cylinders – Day 1

Warm – Up: Read this section and Complete the puzzle on page 2.

Three-dimensional figures, or solids, can be made up of flat or curved surfaces. Each flat surface is called a

face. An edge is the segment that is the intersection of two faces. A vertex is the point that is the intersection

of three or more faces. Each face of a solid figure is called either a base or a lateral face.

Solid figures generally have one or two bases. If it has two, these bases are parallel. If a figure has two parallel

bases and lateral faces, such as in a prism, the bases will be perpendicular to the lateral faces.

A polyhedron is formed by four or more polygons that intersect only at their edges. Prisms and pyramids are

polyhedrons, but cylinders and cones are not.

2

Co

3

Shape Name Formula Example

2.

3.

4.

5.

25 ft

4

Shape Name Formula Example

6.

7.

8.

9.

5

Calculate the volume of each cylinder. Write your answers in terms of and to the nearest tenth.

10. 11.

Working Backwards

12.

13. A cube has a volume of 3375 cubic units. Calculate the length of one side of the cube.

6

14. The volume of a cylinder is 441 in3. The height of the cylinder is 9 in. Calculate the radius of the cylinder

to the nearest tenth of a centimeter.

15. The volume of a cylinder is 794.3 cm3. The height of the cylinder is 7 cm. Calculate the radius of the

cylinder to the nearest tenth of a centimeter.

Challenge

7

Summary:

Exit Ticket:

8

Homework - Volume of Prisms and cylinders – Day 1

Calculate the volume of each.

1.

2.

3.

4.

5.

6. Round your answers to the nearest tenth.

9

7. Round your answers to the nearest hundredth.

8. Leave your answer in terms of .

Word Problems

9. The volume of a cube is 216 cubic yards. Find the side length.

10. Julia has a rectangular prism with a length of 10 centimeters, a width of 2 centimeters, and an unknown height. He

needs to build another rectangular prism with a length of 5 centimeters and the same height as the original prism.

The volume of the two prisms will be the same. Find the width, in centimeters, of the new prism.

11. 12.

10

13.

14. A right circular cylinder has a volume of 2,000 cubic inches and a height of 4 inches. What is the radius of the

cylinder to the nearest tenth of an inch?

15.

11

SWBAT: Calculate the Volume of Pyramids and Cones

Warm - Up

Calculate the volume of the prism below.

a) If the dimensions are doubled.

b) If the dimensions are divided by 5.

Volume of a Pyramids and Cones

12

Shape Name Formula Example

1.

2.

3.

l

13

4.

5.

6.

7.

8.

14

Word - Problems

9. The Volume of a square pyramid is 507 meter cubed. If the height is 9 meters, then find the dimensions of the base?

10. A cube with sides 5 inches, and a pyramid with base edges 5 inches. What is the height, so that the volume of the cube and the pyramid are equal?

11. A right cone has a height of 6 feet and a volume of 32 cubic feet. What is its radius?

12. Sand is piled in the shape of a cone. If a pile of sand has a diameter of 20 feet and a volume of 610

feet cubed, then what is the height of the pile?

15

Challenge

Calculate the volume of the composite figure.

Summary

Calculate the volume of each shape.

a. b.

Exit Ticket

16

Homework - Volume of Pyramids and Cones – Day 2

Calculate the volume of each.

1.

2.

3.

***4.

5.

6.

7.

8.

17

Word Problems

9. The volume of a square pyramid is 605 . Calculate the dimensions of the base of the square if the

pyramid has a height of 15m.

10. The Volume of square pyramid is 784 . If the base edge is 14 centimeters, then how tall is the

pyramid?

11. A cone has a volume of 432 and a height of 9 cm.

a) Calculate the radius of the cone b) Calculate the slant height of the cone.

12. If the volume of a cone is 10 what is its height if the area of the base is 10 m2 ?

18

Surface area of rectangular prisms and cylinders – Day 3

Warm – Up

Rectangular Prism

SA=2lh + 2hw + 2lw This formula assumes a "closed box", with all 6 sides

19

Example 1:

Calculate the surface area of the prism below.

Example 2:

Rashid needs to buy some wood to build a box. He must calculate the surface area of the box to determine how

much wood to buy. A diagram of the box is shown below. How much wood does Rashid need to buy to build

the box?

Example 3: The surface area of the prism below is 102 cm2. Find x

20

Example 4:

Calculate the surface area of a cube with a side that measures 5 in.

Example 5:

The surface area of a cube is 24 cm2. Find the length of each side of the cube.

21

Surface Area of a Cylinder =

Example 6:

Find the surface area, to the nearest tenth of a square foot.

22

7. Calculate the surface area, to the nearest tenth of a square foot.

8. A cylinder has a surface area of 200 ft2.

a) Calculate the radius of the cylinder if the height is 15 feet.

b) Calculate the Lateral Area of the cylinder.

9.

23

Challenge Problem: What is the surface area of the composite figure below?

Summary:

Exit Ticket

24

Homework - Surface area of rectangular prisms and cylinders – Day 3

1. Find the surface area, to the nearest tenth of a square foot, of this container assuming it has a closed top and

bottom.

2. Find the surface area of the prism below.

3. Find the surface area of the cylinder below.

4. Calculate the surface area of a cube with a side of 6 inches.

6 cm

3cm

11cm

25

5. Solve for x given the surface area.

6. A cube has a surface area of 486 cm2. Calculate the length of one side of the cube.

7. The surface area of a cylinder is 48 square feet. The radius of the cylinder is 3 feet. What is the

height of the cylinder?

8. Solve for z given the surface area.

26

Surface area of “Other” prisms – Day 4

Warm – Up

Calculate the surface area of the cube below.

Describe the effect of each change on the surface of the given figure.

a) If the dimensions are doubled.

b) If the dimensions are divided by 5.

10 inches

27

Shape Procedure for Calculating Surface Area

1. Name _______________________

2. Name _______________________

3. Name _______________________

28

4. Name _______________________

5. Name _______________________

6. Name _______________________

29

Word Problems

7.

8.

9.

30

Challenge A builder drills a hole through a cube of concrete, as shown in the figure. This cube will be an outlet for a water tap on the side of a house.

Find the surface area of the figure.

Exit Ticket

Calculate the surface area of the triangular prism to the nearest hundredth.

31

Homework – Day 4

Calculate the Lateral and Surface area of each.

Show your work here!

1.

2.

3.

4.

32

Word Problems

5. The lateral area for a hexagonal prism measures 432 inches2. Calculate the surface area of the prism if

the height of the prism measures 9 inches.

6. The lateral area for a regular triangular prism measures 462 inches2. Calculate the surface area of the

prism if the height of the prism measures 11 inches.

7. The surface area for a right triangular prism measures 864 cm2. The legs of the triangle measure 12 and

16 cm respectively. Calculate the height and Lateral Area of the prism.

(Draw a picture to help you!)

33

Surface Area of Pyramids and Cones – Day 5

Warm – Up

1. 2.

Pyramids

l

34

Example 1: Find the L.A. and S.A.

Example 2:

Example 3: **Challenge***

35

Example 4:

Cones

36

Example 5: Calculate the lateral area and surface area.

Example 6: Calculate the lateral area and surface area.

Word Problems

7. Find the surface area of a regular square pyramid with slant height 7 in, if its lateral area is 70 sq. in.

8. Find the slant height of a regular hexagonal pyramid with base edge length 6 cm, and lateral area 198 cm2

37

9. A cone has a lateral area of 72 and a total surface area of 121. Find its radius.

10. A cone has a lateral area of 34 and a total surface area of 203. Find its radius.

Challenge

Summary

Exit Ticket

38

Day 5 - Homework

Find the Lateral Area and Surface Area of each Prism, Pyramid, and Cone.

1.

2.

3.

4.

5.

6.

39

Word Problems

7.

8.

9. Find the slant height of a regular square pyramid with base edge length 4 cm, if its lateral area is 72 cm2.

10.

40

Day 6 – Spheres

Warm – Up

41

Find the surface area of each sphere. Leave your answers in terms of .

1.

2.

Example 3: Find the surface area of a sphere with a great circle that has an area of 49 mi2.

Example 4: Find the radius of a sphere with a surface area of 1024 u2.

42

Example 5: Find the volume of the sphere. Give your answer in terms of.

Example 6: Find the radius of a sphere with volume 7776 ft3.

Example 7: Find the volume of the sphere if the surface area is represented by 196.

Leave your answer in terms of.

43

Challenge

SUMMARY

Exit Ticket If the surface area of a sphere is represented by 900,

What is the volume in terms of ?

1) 300

2) 3000

3) 4500

4) 36000

44

Day 6 – Homework

Calculate the Surface Area of each. Leave your answers in terms of .

1.

2.

3.

4.

5. The circumference of a great circle of a

sphere is 8 meters. What is the surface

area of the sphere?

6. The area of a great circle of a sphere is

36 meters. What is the surface area of

the sphere?

45

Calculate the Volume of each. Round your answers to 2 decimal places.

7. 8.

9.

10.

11. Calculate the surface area of a sphere

given a volume of 26,244 cubic meters.

12. Calculate the volume of a sphere given a

surface area of 100 square meters.

Round your answer to the nearest tenth.

46

Day 7 – Review

3-D Shape Lateral Area Surface Area Volume

1.

2.

3.

4.

6cm

8 cm

47

3-D Shape Lateral Area Surface Area Volume

5.

6.

7.

8.

9.

48

Day 8 – Word Problems

1. A cube has a volume of 729 cubic units. Calculate the length of one side of the cube.

2. The volume of a cylinder is 600 in3. The height of the cylinder is 6 in. Calculate the radius of the

cylinder to the nearest tenth of a centimeter.

3. The volume of a cylinder is 5428.7 in3. The height of the cylinder is 3 in. Calculate the radius of the

cylinder to the nearest tenth of a centimeter.

4.

5.

Ans: s = 9 units

Ans: r = 10 in

Ans: r 24 in

Ans: h 6 in

Ans: length = 12.5 in

49

6.

Explain your answer below.

7.

Ans: “C” (2)3 = 8

Ans: “A” 100.53 (3)3 = 2714.34

50

8. The base of a pyramid is a rectangle with a width of 8 cm and a length of 9 cm. Find, in centimeters, the

height of the pyramid if the volume is 264 cm3 .

9. The volume of a sphere is 12348 in3. Calculate the radius of the sphere and the surface area of the

sphere.

10.

11.

Ans: h = 11 cm

Ans: r = 21 in

Ans: LA 471.2 squ

Ans: V 1206.4 cu

51

12. A cone has a volume of 432 cm3 and height of 9cm. Calculate the surface area of the cone.

13.

14.

15.

Explain Your Answer!

Ans: SA 1017.9 cm2

Ans: LA 402.1 cm2

Ans: r = 6

Ans: “C” 196 (2)2 = 784

52

SUMMARY

53

Name _________________________ Teacher __________ Class/Period _______________

Due: __________________________

Extra Credit