Converting Area Measurements We already know how to convert between units of linear measurement. Ex. To convert between units of area, we have to remember that area is equal to, or length X width. This means we have to convert BOTH the length AND the WIDTH. This is easier than you might think: all you do is multiply or divide by the conversion factor! Once for the length and once for the width. Ex: 100cm 2 = m 2 1) Find how to convert between cm and m on your conversion chart. 2) To convert the area, we divide by 100 two times Ex: How many square feet are there in a square yard? 1) We know that make a yard, so the length conversion is to multiply by 3 2) To find the area, we must multiply 3 two times (or ) 3) 4) WE can see this in the following diagram (count the square feet): Ex) Convert 30 square feet to square meters. 1) Converting between SI and imperial area units is the same process as the above examples. 2) First, find the conversion factor you need. 3) So we must multiply 30ft 2 by 0.3048 twice: Remember, you need to check if your answer makes sense! Think: Will my answer be more or less? If the unit you are converting to is smaller than the unit you are given, your answer will be than the number you start with. Ex: Convert 5 square metres into square feet 1) Will the answer be more or less than 5? 2) The conversion is 1 ft = 3) Try both dividing and multiplying 5 by the conversion factor: 1
Whiteboard Practice: Convert 50m 2 to cm 2 Convert 23yd 2 to m 2 Remember to check if your answer makes sense! 2
Math 10 3: Feb 24th Outline for the day: 1. Area word problems practice 2. Review/catch up (QUIZ TOMORROW!) 3
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Area Word Problems Ms. Kierstead wants to lay grass on her acreage property. If her property is 250 m by 300 m how much land needs to be covered? Draw a picture. Shelley is trying to decide whether to put hardwood flooring or carpet on her living room floor. The dimensions of the room are 22 ft by 16 ft. The hardwood flooring costs $18.99 / m 2 with an installation cost of $1500.00. The carpet costs $21.95 / yd 2 with an installation cost of $1350.00. Which type of flooring costs less? 5
You try: Irina purchased a farm in Saskatchewan. She wants to plant balsam fir seedlings, and she estimated the field measures 72 yards by 65 yards. The tree nursery manager told her that each seedling requires an area of 64 ft 2 to grow properly. How many seedlings can Irina plant on her acre of land? 6
Math 10 3: Day 15 Outline for the day: 1. Lesson on circumference and area of circles 2. Circles practice and assignment 7
5 cm 2 = 0.007 m 2 8
Circumference and Area of a Circle All the points on a circle are equidistant (the same distance) from the of the circle. A line that passes through the center of a circle and touches the edge of the circle on both sides is called the. A line that starts at the center of the circle and touches an outside edge is called the. ACTIVITY: Using the string, a ruler and the circular shapes 9
1 2 3 Circle Circumference Use a licorice whip to measure Diameter (d) use a ruler to measure Compare: C/d 10
How can we calculate radius, diameter, and circumference? The radius can be calculated by dividing the diameter by 2 The diameter can be calculated by multiplying the radius by 2 The of a circle is the perimeter of the circle. It can be calculated with the formula : Where C = circumference (perimeter) = pi a constant that is 3.14. d = diameter Ex) What is the circumference of a circle with a diameter of 8 cm? Ex2. What is the circumference of a circle with a radius of 2.5 mm? How can we calculate the area of a circle? Use the formula A=πr 2 This means we need to know the radius Ex) What is the area of the following circle: Ex) What is the area of the following circle: 11
Practice: 1) What is the circumference of a circle with a radius of 2cm? 2) What is the area of the circle with a radius of 2cm? 12
Journals: One thing I need to practice before the quiz tomorrow is... One thing I need help with is... 13
Math 10 3: Day 16 Outline for the day: 1. Review for quiz: any last questions? 2. Perimeter and area quiz 3. Surface area of prisms 14
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Math 10 3: Day 17 Outline for the day: 1. Review surface area of prisms 2. Lesson on surface area of cylinders and cones and practice 3. Surface area assignment 16
Surface Area Surface area is the total area of all the sides in a 3D object added together. One of the easiest ways to get a simplified formula for surface area is to look at the net of the shape. Rectangular Prism We need to find the area of each side (a total of 6 sides), and then add them all up Ex) Find the surface area of the following rectangular prism. Triangular Prism Find the area of the triangular ends. Remember, the formula for the area of a triangle is Then find the area of the 3 rectangular sides Add all the sides together Ex) Find the surface area for the following triangular prism. 17
Practice: Find the surface area of the following triangular prism 6ft 2ft h= 1.6ft 18
Whiteboard Review: find the surface area of the rectangular prism 7cm 1cm 2cm 19
Surface Area of Cylinders and Cones Cylinder: We need to find the area of the top, bottom, and sides. 1) The top and bottom are circles, so the formula for the area of both together is: 2) The side is a rectangle that is wrapped around. The base of the rectangle is the circumference of the circles and the height is the height of the cylinder. This means that the area of the side is: 3) To find the total surface area of the cylinder, add the area of the top and bottom to the area of the side. 20
Ex) Find the surface area of the following cylinder 30cm Diameter = 10cm 21
Whiteboard Practice: Radius =3cm Height= 5cm 22
Cones Find the area of the circle at the bottom of the cone: Find the area of the top. The formula is: Add the two areas together to find the total area 23
Ex) Find the surface area for the following cone. Radius = 3cm 6cm 24
Whiteboard Practice: Radius =3cm S= 5cm 25
Complete the Surface Area Assignment 26
Math 10 3: Day 18 Outline for the day: 1. Quick surface area review 2. Aluminum foil prank? 27
Question: Can we cover everything in this room in aluminum foil for under $50? Group 1: desks, chairs, floor Group 2: my desk, computer, chair Group 3: cabinets, filing cabinet, fridge Group 4: tables, bins, bulletin boards 28
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