Chp1 Measurement. = 168 in. notice ft cancels and we are left with. 4.25, so 4ft exactly, ignore the decimal. Math 10 Pre-Calc &Foundations

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1 Chp1 Measurement 1.1 Imperial Measurement used in construction and in America mostly. Skill converting with in Imperial, using the unit conversion method Common Conversion Factors Ex#1 convert 14ft to inches note: 1ft = 12 in Start x Conversion Factor as a fraction = answer inches! x = 168 in. notice ft cancels and we are left with Ex#2 convert 51 inches into ft and in feet how many feet are in 51in? note: 1 ft = 12 in 4.25, so 4ft exactly, ignore the decimal How many inches is 4 ft? Convert this back to inches to find out. 48. Inches the "left over" inches is the difference of the initial So, 51 4, 3

2 Ex#3 convert 51 inches into yd's, ft and in yards how many yards are in 51in? note: 1 yd = 36 in 1.416, so 1 yd exactly, ignore the decimal How many inches is 1 yd? Convert this back to inches to find out.(this is easy 1yd = 36in) or 36. Feet the "left over" inches is the difference of the initial Note: must people can tell that 15 in = 1ft, 3 in details however. Then we are done, I will show the So, convert 15 in to ft note: 1ft = 12 in 1.25, so 1 ft exactly, ignore the decimal How many inches is 1ft? Convert back to inches to find out. (this is easy 1ft = 12in) or 12 Inches the final left over inches is Final answer is; 1yd, 1ft, 3in. Do Qn's p.25#3,4

3 1.2 Measuring Length and Distance measuring using different systems. Imperial Unit Abbreviation Referent Relationship between units Inch in. Thumb length Foot ft. Foot length 1 ft. = 12 in. Yard yd. Arm Span 1 yd. = 3 ft. Or 1 yd. = 36 in. Mile mi. Distance walked in 20 minutes 1 mi. = 1760 yd. Or 1 mi. = 5280 ft. SI Unit Abbreviation Referent Conversion Factor Meter m Distance from a door knob to the 1 m = 100 cm 1 m = 1000 mm floor Centimetre cm Width of a paper 1 cm = 0.01 m clip millimetre mm Thickness of a dime Or Thickness of a fingernail 1 cm = 10 mm 1 mm = m 1 mm = 0.1 cm

4 Vernier Calipers To Read Vernier calipers: 1. Check where the first line on the moving scale lands. It will point to a place on the fixed scale. This position determines the first digits of the reading. 2. Find the last digit of the reading by examining which line on the moving scale aligns best with a line on the fixed scale. The line on the moving scale determines the last digit. Ex. #1: Read the following Vernier caliper measuremen nts. (a) scale =.01 So, = 4.61 (b) First line = 4.6 next line matches up best with fixed No Qn's

5 1.3 Converting Between Imperial and Metric use your "formula sheet" to convert between the two unit systems. You should be used to using this sheet because this is all you will have for the provincial exam. Ex1. Convert 16 in to cm note: 1in = 2.54 cm Start x Conversion Factor as a fraction = answer Ex2. Convert 27 km to mi. Note: 1mi = km Double unit conversion These questions can be done in multiple ways, but always try converting to as large of a unit as possible to avoid doing a triple unit conversion. Ex3. Convert 2,000 cm to yd's. Try cm to m, then m to yds. Note: 1m = 100cm, 20, now m to yds. Note: 1yd = m Ex4. Convert 75 cm to feet and inches. Note: if you're converting to multiple units as your answer, you need to start your question in the smallest of those units. So, convert to inches first! Note: 1 in = 2.54 cm. so 30 in feet how many feet are in 30 in? note: 1 ft = 12 in 29.53, #, 2.5, so 2 ft exactly, ignore the decimal How many inches is 2 ft? head) Convert this back to inches to find out. (this could be done in your 24. Inches the "left over" inches is the difference of the initial So, 75 2, 6 Do Qn's p.25#7+8

6 1.4 Surfaces Areas of Right Pyramids and Right Cones the surface area of any is the sum or all the individual shapes which you can touch. Use the formula sheet, especially for the surface area of a cone. Also, we use the slant height for surface area questions, not the interior height. Ex1. The surface area is then the 4 sides which are 4 equal triangles and the base which is a square. 4 Triangles h=slant height Square Ex2. If the Slant height is not given, just the interior height, then use Pythagoras' Theorem to find it. So, the slant height = 7.8 in 2

7 Ex3. The surface area of a Right Cone is the area of a circle plus the Lateral area of a cone. Lateral Area Area of a Circle Do Qn's p.54 # 1+2

8 1.5 Volumes of Right Pyramids and Right Cones use the formula sheet you have for these formulas. However in general the equation for the volume of a shape which cones to an apex or point is: Note: the height use for volumes is the "interior height" not the slant height Right Pyramids Ex1. Right Cones

9 Ex2. Finding the Volume if given the slant height, not the interior height Do Qn's p.54 #4&5

10 1.6 Surface area and Volume of a Sphere and Hemisphere take note that your formula sheet has the equations for the S.A. and Volume of a sphere, but not a Hemisphere. The Volume of a hemisphere is just half that of a sphere, however the S.A. of a hemisphere is not just half that of a sphere it includes a S.A. of a circle too, think the "lid" of a bowl. Ex1. Ex2.

11 Finding the Radius if given the Surface Area Ex3. Hemispheres Ex4. Find the Surface Area of this Hemisphere Solution Use the formula:

12 1.7 Solving Problems Involving Compound Objects when finding the Volume of composite shapes you take the sum of the shapes involved. - When finding the Surface Area you take the sum of all the individual 2D shapes which you see or could touch. Volume

13 Surface Area Do Qn p.67 #4

14 Chp1 Study Guide