Perimeter, Area, and Volume · Perimeter, Area, and Volume Name: ... HW: Pgs: 7- 8 DAY 2: ... 37 Homework - Surface area of rectangular solids and cylinders ...

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Algebra 2012 - 2013

Perimeter, Area, and

Volume

Name:______________________________

Teacher:____________________________

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Table of Contents

DAY 1: SWBAT: Calculate the area and perimeter of polygons and circles

Pgs: 1 - 6

HW: Pgs: 7- 8

DAY 2: SWBAT: Calculate the area of composite regions

Pgs: 9 - 15

HW: Pgs: 16 - 18

DAY 3: SWBAT: Calculate the volume of rectangular solids and cylinders

Pgs: 19 - 24

HW: Pgs: 24 - 25

DAY 4: SWBAT: Calculate the missing dimensions of a three dimensional solid using Volume

Pgs: 26 - 30

HW: Pgs: 31 - 32

DAY 5: SWBAT: Calculate the surface area of rectangular solids and cylinders

Pgs: 33 - 36

HW: Pgs: 37 - 38

Formula Sheet: Page 39

Area (triangle)

Area (rectangle)

= (length)•(width)

Area (square)

Area (parallelogram)

Area (trapezoid)

Area (circle)

1

Day 1: Area and Perimeter

SWBAT: Calculate the area and perimeter of polygons and circles

Practice Problems: Calculate the area and the perimeter of the polygons and circles below.

Examples Perimeter Area

1.

2.

3.

2

Examples Perimeter Area

4.

5.

6.

7. Semicircle

3

Circle Problems

7. A circle’s circumference is 22π.

(a)What is the radius of the circle?

(b)What is the diameter of the circle?

8. A circle’s Area is 25π.

(a)What is the radius of the circle?

(b)What is the diameter of the circle?

Example 2: Perimeter Problems

4

Practice Problems: Perimeter Problems

9.

10.

Example 3: Perimeter Word Problems

The length of a rectangle is 5 cm less than three times its width. If the

perimeter of the rectangle is 54 cm, find the length and width.

5

Practice Problems: Perimeter Problems

11. The length of a rectangle is 9 cm more than the width. The perimeter is 78

cm. Find the length and the width.

Regents Problem

Summary

Challenge

6

SUMMARY

Exit Ticket

7

Homework - Perimeter, Circumference, & Area Formulas (Day 1)

8

9

Day 2: SWBAT: Calculate the perimeter and area of Composite shapes

Perimeter & Area of Composite Shapes – Day 2

Warm – Up

Example 1: Determine the perimeter of the following figure below.

10

Practice Problems: Determine the perimeter of the following figure below.

1)

2) Determine the perimeter of the following figure below.

3)

11

Recall, these Area Formulas:

3)

Let’s look at Shaded Area Problems:

12

Directions: Calculate the area of the shaded region in terms of π and to the nearest integers.

4)

5)

6)

A =

A =

13

Challenge Problem #1:

Calculate the area of the shaded region to the nearest integers.

Challenge Problem #2 Bill wishes to replace the carpet in his living room and hallway with laminate flooring. A floor plan is shown.

(a) Find the total area of floor to be recovered.

(b) Laminate flooring comes in boxes that contain 2.15m2 of material. How many boxes will Bill require?

(c) One box costs $ 43.25. How much will the flooring cost?

14

Summary

15

Exit Ticket

1.

2.

16

Homework - Perimeter & Area of Composite Figures – Day 2

2.

17

3.

4.

18

5.

6.

7.

19

SWBAT: Calculate the volume of rectangular solids and cylinders

Volume of rectangular solids and cylinders – Day 3

Warm – Up

The dimensions of a square are measured to be 5.1 inches. The actual dimensions are 5.2 inches. What is the

relative error, to the nearest thousandth, in calculating the area of the square?

Example 1: Calculating Volume

10 cm

20

Practice Problems:

1)

2)

Example 2: Calculating Volume (Working Backwards)

Calculate the height of a rectangular prism with length 13 cm, width 3 cm, and volume 195 cm3.

Practice: Calculating Volume (Working Backwards)

3) Calculate the length of a rectangular prism with height 9 ft, width 15 ft, and volume 3375 ft3.

21

Example 3: Calculate the volume of the cylinder. Give your answers in terms of and rounded to the nearest tenth.

Practice: Calculate the volume of the cylinder. Give your answers in terms of and

rounded to the nearest tenth.

4) 5)

6. Find the volume of a cylinder with a diameter of 16 in. and a height of 17 in. Give your answer

both in terms of and rounded to the nearest tenth.

22

Regents Question

Challenge Problem:

23

Summary:

24

Exit Ticket:

Homework - Volume of rectangular solids and cylinders – Day 3

1) 2)

3)

25

4) Calculate the height of a rectangular prism with length 5 ft, width 9 ft, and volume 495 ft3.

5) 6)

7)

26

SWBAT: Calculate the volume of rectangular solids and cylinders

Volume of rectangular solids and cylinders – Day 4

Warm - Up

Example 1: A cube has a volume of 216 cubic feet. Calculate the side of the cube.

Practice: A cube has a volume of 512 cubic feet. Calculate the side of the cube.

27

Example 2:

Practice

The cylinder below has a volume of 225 cubic inches. Calculate the height of the cylinder with a radius of 5 inches.

Example 3: The cylinder below has a volume of 360 cubic inches. Calculate the radius of the cylinder with a height of 10 inches.

28

Practice: The cylinder below has a volume of 392 cubic inches. Calculate the radius of the cylinder with a height of 8 inches.

Example 4:

Practice:

29

Practice:

Regents Level Question

30

Challenge

Summary

Exit Ticket

Calculate the radius of the cylinder.

31

Day 4 - HW: Working Backwards with Volume

1.

2. 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.

3. 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.

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

32

5.

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

cylinder to the nearest tenth of an inch?

7.

33

SWBAT: Calculate the surface area of rectangular solids and cylinders

Surface area of rectangular solids and cylinders – Day 5

Warm – Up

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.

Rectangular Solid

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

Cylinder

This formula assumes a "closed container", with a top

and bottom..

Example 1: Calculate the surface area of the prism below.

7cm

2cm

4cm

34

Example 2:

Find the surface area, to the nearest tenth of a square foot, of this container assuming it has a

closed top and bottom.

Practice Problems: Try these on your own!

1. 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?

2. Calculate the surface area, to the nearest tenth of a square foot, of this container assuming it has

a closed top and bottom.

8in

3in

35

3. A student says the two cylinders below have the same surface area. Is the student correct?

4. 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?

5. Regents Problem

6 in

8 in 6 in

8 in

36

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

Summary:

Exit Ticket

37

Homework - Surface area of rectangular solids and cylinders – Day 5

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 prism below.

4.

9 m

6 m

6 cm

3cm

11cm

3.7ft

6.1 ft

8.4 ft

38

5)

6)

7) A rectangular prism has a measured length of 24 meters, a width of 13 meters and a height of 18 meters. The

actual length is 24.04 meters; width is 13.04 meters; and height of 18.04 meters. What is the relative error of

the surface area of the prism?

8)

39

FORMULA SHEET

𝑜𝑟 𝐶 = 𝜋𝑑

SA = 6s2

V = s3

s