10B Apple Yoyo Jack Ikaros Measurement 10B Apple Yoyo Jack Ikaros

Content 1.1 Imperial Measure of length 1.3 Relating SI and I mperial Units 1.4 SA of 3-D Shapes ~_~ 1.5 Volumes of 3-D Shapes ~_~

Today’s objects 1.1 Imperial Units(in. yd. ft. mi.) Referent Abbreviation Unit analysis SI system measures(We are going to talk about it later.) Proportional reasoning 1.2 Measuring instruments 1.4 Convert measurements between SI units and imperial units SI units 1.4 Right pyramid Apex Slant height Polygon base Lateral area Right cone 1.5 Cylinder Right prism Base area Cone Radius 1.6 Sphere Surface area Volume Hemisphere 1.7 Substitute Composite Objects

Presentation Plan(Today’s objects) Review how to: Convert the units Imperial units with Imperial units——Jack Imperial units with SI units——Ikaros Calculate the surface area of 3-D shapes——Yoyo Right Cone Right Pyramid Right Prism Right Cylinder Sphere Hemisphere Calculate the volumes of 3-D shapes(above-mentioned)—— Yoyo Solving Problems Involving Objects——Apple Example Questions Quiz Time!10-15minutes/7 questions(multiple-choice)No written!

READY?

1.1 Imperial Measure of length Develop personal referents to estimate imperial measures of length

Let’s figure it out. Imperial Unit Abbreviation Referent Relationship between Units inch in. Thumb length foot ft. Foot length 1ft.=12in. yard yd. Arm span 1yd.=36in.=3ft. mile mi. Distance walked in 20 min 1mi.= 1760yd.= 5280ft. Let’s figure it out.

Use the previous graph to solve the following problems A)convert 5 yd. to inches and feet B)convert 51 in. to (1)feet and inches (2)yards, feet, and inches Think about proportional reasoning(the relations between units) e.g.12in.=12in.*(1/12)=1ft. Use the previous graph to solve the following problems

Solution A)5yd.=5*3ft=15ft.=15* 12ft=180in. B)51in.=51/12ft.=(4+ 3/12)ft.=4ft.3in.=1yd.1ft. 3in. Solution

Let’s make it a bit more difficult. Convert 12yd.32ft.144in. into yd. ft. Let’s make it a bit more difficult.

The answer is……. 144in.=12ft. 12ft+32ft.=44ft.=14yd.2ft. 14yd.+12yd.=26yd. So the answer is 26yd.2ft. The answer is…….

26yd.2ft.=960in. 12yd.32ft.144in.=960in. correct How can we verify it?

What do we call this? Unit analysis. -Is one method of verifying that the units in a conversion are correct. What do we call this?

1.3 Relating SI and Imperial Units SI UNIT Millimetre(mm) Centimetre(cm) Metre(m) Kilometre(km) IMPERIAL UNIT Inch(in) Foot(ft) Yard(yd) Mile(mi)

Relationships brtween imperial units and SI units 1km=1000m 1mi=1760yd =5280ft =63360 in 1m=100cm 1yd=3ft=36in 1cm=10mm 1ft=12in 1m=1000mm 1in=0.083333ft 1m=10dm 1ft=0.3333yd SI Units to Imperial Units Imperial Units to SI units 1mm≈0.04in 1in=2.54cm 1cm≈0.4in 1ft≈30cm 1ft≈0.3m 1m≈39in 1m≈3.25ft 1yd=91.44cm 1yd≈0.9m 1km≈0.6mi 1mi≈1.6km

Example I A lane is approximately 19m long. What is this measurement to the nearest foot? (1m≈3.25 ft.) From the table,1m≈3.25 ft. So,19m≈19 x (3.25) ft. 19m≈62 ft. A length of 19m is approximately 62 ft.

Example II Convert 6 ft. 2 in. to inches (1ft=12in) 1 ft. = 12 in. So, 6 ft. = 6×12 in. 6 ft. = 72 in And, 6 ft. 2 in.=72 in. + 2 in. =74 in.

Example Ⅲ htruck =3.5m=350cm 350cm×0.4 in.=137.8 in A truck driver knows that his truck is 3.5m high.The support beams of a bridge are 11ft.9in. high. Can the truck cross the bridge smoothly? (1cm≈0.4in) htruck =3.5m=350cm 350cm×0.4 in.=137.8 in hbridge =11ft.9in=141in＞137.8in hbridge＞htruck Yes! It can~

Surface Area 1.4 SA of 3-D Shapes ~_~ Area is the two-dimensional (2-D) size of a surface. Surface area (SA) of a solid is the total area of the exposed surfaces of a three-dimensional (3-D) object.

Surface Area Formulas Right Cone ASide= πrs ABase= πr2 SA = πr2 + πrs

Surface Area Formulas Square-based Pyramid Atriangle = ½ bs Abase = b2 SA = 2bs + b2 General Right Pyramid SA = sum of all the areas of all the faces b S ~Pyramid head~

Surface Area Formulas Rectangular Prism SA = 2(hl + lw + hw)

Surface Area Formulas Right Cylinder Atop=πr2 Abottom=πr2 Aside=2πrh SA=2πr2 + 2πrh

Example Questions 1. Which expression could be used to calculate the surface area of the right square-based pyramid with a base length of 10 cm and a height of 12 cm? *SA = 2bs + b2 S= 13 h=12 5 b=10

Example Questions 2. Raj was asked to make a cylindrical tank with a lateral surface area of 2622 m 2 and a height of 23 m. Which net diagram below would be correct for this cylinder? *Lateral SA= Aside=2πrh 2πrh=114×23=2622

1.5 Volumes of 3-D Shapes ~_~ is the space that a shape occupies often quantified numerically using the SI unit , the cubic meter.

Volume Formulas Right Cone ABase= πr2 V=1/3(area of base)h =1/3πr2h

Volume Formulas General Right Pyramid V = 1/3(area of base) h Square-based Pyramid V = 1/3b2h Right Rectangular Pyramid V = 1/3lwh ~Pyramid head~

Volume Formulas General Right Prism Rectangular Right Prism V=(area of base)h Rectangular Right Prism V=lwh General Right Prism Rectangular Prism

Volume Formulas Right Cylinder Abase=πr2 V=(area of base)h =πr2h

Example Questions (*Vcylinder= πr2 h) 3. Which of the following expressions represents the volume of the cylinder below? (*Vcylinder= πr2 h) d=2x+4 So, r=1x+2 V= πr2 h=π(1x+2) 2 (3x-1 ) …… It’s “C”!

What is it ??? Definition of sphere: A sphere is the set of points which are all the same distance from a fixed point which is the centre in space. A line segment that joins the centre to any point on the sphere is a radius. A line segment that joins two points on a sphere and passes through the centre is a diameter. What is it ???

The surface area, SA, of a sphere with radius r is : SA = 4πr Surface Area of a Sphere The surface area, SA, of a sphere with radius r is : SA = 4πr 2

The surface area, SA, of a hemisphere with radius r is : SA=3πr 2 Surface Area of a Hemisphere The surface area, SA, of a hemisphere with radius r is : SA=3πr 2

The diameter of a baseball is approximately 3 in The diameter of a baseball is approximately 3 in. Determine the surface area of a baseball to the nearest square inch. Here is the example:

Solution: Use the formula for the surface area of a sphere. The radius is: ½(3 in.) = 1.5 in. SA = 4πr2 SA = 4π(1.5)2 SA= 28.8 The surface area of a baseball is approximately 28 square inches.

The volume, V, of a sphere with radius r is : V =4/3πr Volume of a Sphere The volume, V, of a sphere with radius r is : V =4/3πr 3

Example: The sun approximates a sphere with diameter 870 000 mi. What is the approximate volume of the sun?

Solution: Use the formula for the volume of a sphere. The radius, r, is: r = ½ (870 000mi.) r = 435 000mi. V = 4/3 πr 3 V = 4/3 π(435 000mi.) 3 V = 3.4479 * 10 17

1.7 Solving Problems Involving Objects

Example: Determine the volume of this composite object to the nearest tenth of a cubic meter.

First The object comprises a right rectangular prism and a right rectangular pyramid. Use the formula for the volume of a right rectangular prism. V= lwh V=(6.7)(2.9)(2.9) V= 56.347 Solution: Then Use the formula for the volume of a right rectangular pyramid. V= 1/3 lwh V= 1/3(6.7)(2.9)(2.1) V= 13.601 Volume of the composite object is: 56.347 + 13.601= 69.948The So, the volume of the composite object is approximately 69.9 m3.

That’s all in the chapter 1 Easy Right?

NO MORE Q? So, that’s all we need to teach you today. Let’s have a xiao quiz~

QUIZ TIME! Remember to… Choose “C”!