UNIT 6 – MEASUREMENT

Date Lesson Text TOPIC Homework

May 2 6.1 8.1 The Pythagorean Theorem Pg. 423 # 1ac, 2ac, 3ab, 4ac, 5, 7, 8, 10

May 4 6.2 8.2 Perimeter and Area (NO CIRCLES) Pg. 432 # 1acde, 2abdf, 3, 4, 11, 14, 18

May 7 6.3 8.2 Working with

Perimeter and Area of CIRCLES

WS 6.3

Pg. 432 # 1b, 2ce, 10, 12, 15, 17

May 8 6.4 8.3 SA of Prisms & Pyramids Pg. 441 # 1, 3, 5a, 7b, 11bc, 16

May 9 6.5 8.3 Volume of Prisms & Pyramids Pg. 441 # 2, 4, 5b, 6, 7a, 9, 10a, 11a

May 10 6.6 Surface Area of Cylinders WS 6.6

May 11 6.7 8.4 Surface Area of a Cone Pg. 447 # 1bc, 2 - 10

May 14 6.8 8.5 Volume of Cylinders and Cones Pg. 454 # 1bd, 2b, 3, 4, 5, 7, 8b, 9

May 15 6.9 8.6 Surface Area and Volume of Spheres Pg. 459 # 1ad, 2b, 3, 4 ,5a, 8

Pg. 465 # 1 - 4, 7, 8

May 16 6.10 Measurement Worksheet WS 6.10

May 17 6.11 Unit 6 Review Pg. 470 # 1 - 15

May 18 6.12

UNIT 6 TEST

MPM 1D Lesson 6.1 Pythagorean Theorem

The sum of the squares of the legs is equal to the square of the hypotenuse.

This relationship is written as: a2 + b

2 = c

2, where c is the hypotenuse.

This relationship is named the Pythagorean Theorem.

The theorem is true for right triangles only.

This relationship can be used to determine the length of an unknown side of a right triangle when you know the lengths of the other two sides.

To determine the hypotenuse in this right triangle, substitute for a and b in

the formula a2 + b

2 = c

2. Substitute: a = 7 and b = 5

We can also use the Pythagorean Theorem to determine the length of a leg.

Ex. Kim is building a ramp with a piece of wood 175 cm long. The height of the ramp is 35 cm.

What is the horizontal length of the ramp?

Ex. Find the length of each unknown side. Round your answer to 1 decimal place when necessary.

a) b)

c) d)

Ex. Do the following lengths form a right triangle?

a)

b)

c) a = 6.4, b = 12, c = 12.2

Pg. 423 # 1ac, 2ac, 3ab, 4ac, 5, 7, 8, 10

MPM1D Lesson 6.2 Perimeter and Area

For each of the following, round your answer to 1 decimal place where necessary.

Ex. Find the perimeter and area of each of the following:

a) b)

c) d)

Pg. 432 # 1acde, 2abdf, 3, 4, 11, 14, 18

MPM1D Lesson 6.3 Area and Perimeter - Working With

Simplify:

1. 234 2. 128 3. 12735

4. 752522

5. 2

1042

6.

3

652

7.

3

562

8.

3

522

9. 52

3

1 2

10. 1223

4 3 11.

3

2343

12.

3

601043

Solve for r. (Exact answer required. No calculator needed)

1. 2 10r 2. 2 11r 3. 2 11r 4. 2 10r

5. 24 11r 6. 24 10r 7. 24

113

r

Use a calculator to evaluate to 2 decimal places:

1. 128 2.

3

652

3.

3

263

4.

3

4243

Ex. Find the area and perimeter of each of the following.

a) b)

MPM1D Lesson 6.4 Surface Area: Prisms and Pyramids

Surface Area is a measure of: ______________________________________________

______________________________________________________________________ .

Surface Area of a Prism is: __________________ Surface Area of a Pyramid is __________________

Eg) Determine the Surface Area of each object:

a) b)

c)

Pg. 441 # 1, 3, 5a, 7b, 11bc, 16

MPM1D Lesson 6.5 Volume: Prisms and Pyramids

The volume of a prism depends on two things: 1. ____________________________________

2. ____________________________________

The volume of a prism is: __________________________________

The volume of a pyramid is: __________________________________

Calculate the volume of each of the following:

b) b)

c) d)

CHALLENGE: How many litres are in a cubic metre if one mL is equal to one cubic cm? Pg. 441 # 2, 4, 5b, 6,

7a, 9, 10a, 11a

MPM1D Lesson 6.6 Surface Area of Cylinders

The Surface Area of any 3-dimensional object is determined by calculating the sum of the areas of all its faces. Cylinder

The surface area of a cylinder consists of 2 circles and a rectangle. The width of the rectangle is equal to the circumference of the base of the cylinder. The surface area of a cylinder is calculated using the formula:

22 2SA r rh

Ex. 1 A cylinder has a radius of 10 cm and a height of 15 cm. Calculate its surface area.

Watch out for questions in which only part of the surface area formula is needed.

Ex. 2 A soup can has a height of 10 cm and a diameter of 7 cm.

a) How much tin is needed to make the can?

b) How much paper is needed to make the label?

WS 6.6

MPM1D Lesson 6.7 Surface Area of Cones

A cone is comprised of two parts: a circular base and a curved surface (called the lateral surface).

The formula for the Surface Area of a Cone is: _______________________________________ .

Calculate the Surface Area of each cone:

a) b)

Eg)

Pg. 447 # 1bc, 2 - 10

MPM1D Lesson 6.8 Volume: Cylinders and Cones

“Cylinder” is the name we give a ______________________________________ .

Using our knowledge of prisms, we can determine a formula for the volume of cylinders:

________________________________________

The relationship between cylinders and cones is similar to the relationship between rectangular prisms and

pyramids. The formula for the volume of cones is:

________________________________________

Calculate the volume of each of the following:

a)

b)

c) d)

Pg. 454 # 1bd, 2b,

3, 4, 5, 7, 8b, 9

MPM1D Lesson 6.9 Spheres: Surface Area and Volume

Surface Area: Volume:

Ex. Find the Surface Area and Volume of each of the following spheres:

a) b)

Ex. Find the radius of a sphere with Surface Area 452.4 cm2.

Ex. What happens to the Surface area of a sphere if its radius is

a) doubled? b) tripled?

Pg. 459 # 1ad, 2b, 3,

4 ,5a, 8

Pg. 465 # 1 - 4, 7, 8