Name:__________________________________________________ Date: _______________
Algebra 2012 - 2013
Perimeter, Area, and
Volume
Name:______________________________
Teacher:____________________________
Pd: _______
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
