Date Lesson Text TOPIC Homework. SA of Prisms & Pyramids Pg. 441 # 1, 3, 5a, 7b, 11bc, 16. Surface Area of Cylinders WS 6.6

Transcription

1 UNIT 6 MEASUREMENT Date Lesson Text TOPIC Homework May May The Pythagorean Theorem Pg. 4 # 1ac, ac, ab, 4ac, 5, 7, 8, 10 Perimeter and Area (NO CIRCLES) Pg. 4 # 1acde, abdf,, 4, 11, 14, 18 May Working with Perimeter and Area of CIRCLES WS 6. Pg. 4 # 1b, ce, 10, 1, 15, 17 May SA of Prisms & Pyramids Pg. 441 # 1,, 5a, 7b, 11bc, 16 May Volume of Prisms & Pyramids Pg. 441 #, 4, 5b, 6, 7a, 9, 10a, 11a May May May May May May Surface Area of Cylinders WS 6.6 Surface Area of a Cone Pg. 447 # 1bc, - 10 Volume of Cylinders and Cones Pg. 454 # 1bd, b,, 4, 5, 7, 8b, 9 Surface Area and Volume of Spheres Pg. 459 # 1ad, b,, 4,5a, 8 Pg. 465 # 1-4, 7, 8 Measurement Worksheet WS 6.10 Unit 6 Review Pg. 470 # 1-15 May UNIT 6 TEST

2 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: a + b = c, 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 a + b = c. Substitute: a = 7 and b = 5

3 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 5 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)

4 Ex. Do the following lengths form a right triangle? a) b) c) a = 6.4, b = 1, c = 1. Pg. 4 # 1ac, ac, ab, 4ac, 5, 7, 8, 10

5 MPM1D Lesson 6. 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)

6 c) d) Pg. 4 # 1acde, abdf,, 4, 11, 14, 18

7 MPM1D Lesson 6. Area and Perimeter - Working With Simplify: Solve for r. (Exact answer required. No calculator needed) 1. r 10. r 11. r r r r r 11

8 Use a calculator to evaluate to decimal places: Ex. Find the area and perimeter of each of the following. a) b)

9 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,, 5a, 7b, 11bc, 16

10 MPM1D Lesson 6.5 Volume: Prisms and Pyramids The volume of a prism depends on two things: 1.. 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 #, 4, 5b, 6, 7a, 9, 10a, 11a

11 MPM1D Lesson 6.6 Surface Area of Cylinders The Surface Area of any -dimensional object is determined by calculating the sum of the areas of all its faces. Cylinder The surface area of a cylinder consists of 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: SA r rh Ex. 1 A cylinder has a radius of 10 cm and a height of 15 cm. Calculate its surface area.

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

13 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, - 10

14 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, b,, 4, 5, 7, 8b, 9

15 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 45.4 cm. Ex. What happens to the Surface area of a sphere if its radius is a) doubled? b) tripled? Pg. 459 # 1ad, b,, 4,5a, 8 Pg. 465 # 1-4, 7, 8