Measurement

10B Apple Yoyo Jack Ikaros

Content

1.1 Imperial Measure of

length1.3 Relating SI and I mperial Units

1.4 SA of 3-D Shapes ~_~

1.5 Volumes of 3-D Shapes ~_~

Today’s objects1.1 Imperial Units(in. yd. ft.

mi.) Referent Abbreviation Unit analysis SI system measures(We

are going to talk about it later.)

Proportional reasoning1.2 Measuring instruments1.4 Convert measurements

between SI units and imperial units

SI units

1.4 Right pyramid Apex Slant height Polygon base Lateral area Right cone1.5 Cylinder Right prism Base area Cone Radius

1.6 Sphere Surface area Volume Hemisphere1.7 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

figu

re it

ou

t.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.

Use

the

prev

ious

gr

aph

to so

lve th

e fo

llowi

ng p

robl

ems

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.

Solu

tion A)5yd.=5*3ft=15ft.=1

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

Let’s

mak

e it

a bi

t mor

e di

fficu

lt. Convert 12yd.32ft.144in. into yd. ft.

The

answ

er

is……

. 144in.=12ft. 12ft+32ft.=44ft.=14yd.2ft. 14yd.+12yd.=26yd.

So the answer is 26yd.2ft.

How

can

we

verif

y it? 26yd.2ft.=960in.

12yd.32ft.144in.=960in.

correct

Wha

t do

we ca

ll th

is? Unit analysis. -Is one method of verifying that the units in a conversion are correct.

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)

SI Units to Imperial Units

Imperial Units to SI units

1mm≈0.04in 1in=2.54cm

1cm≈0.4in 1ft≈30cm1ft≈0.3m

1m≈39in1m≈3.25ft

1yd=91.44cm1yd≈0.9m

1km≈0.6mi 1mi≈1.6km

Relationships brtween imperial units and SI units

SI Units Imperial 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

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 inAnd, 6 ft. 2 in.=72 in. + 2

in. =74 in.

Example ⅢA 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~

1.4 SA of 3-D Shapes ~_~

Surface Area 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 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 Questions1. 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

b=10

h=12

5

Example Questions2. 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=2πrh2πrh=114×23=2622

1.5 Volumes of 3-D Shapes ~_~

Volume 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

~Pyramid head~

General Right Pyramid V = 1/3(area of base) h

Square-based Pyramid V = 1/3b2h

Right Rectangular Pyramid V = 1/3lwh

Volume Formulas General Right Prism

V=(area of base)h Rectangular Right Prism

V=lwh

Rectangular Prism

General Right Prism

Volume Formulas Right Cylinder

Abase=πr2

V=(area of base)h =πr2h

Example Questions3. 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”!

Definition of sphere:

What is it ???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.

Surface Area of a Sphere

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

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. 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 = 4πr2SA = 4π(1.5)2SA= 28.8The 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

3

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

Example:

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

Solution:

1.7 Solving Problems Involving Objects

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

FirstThe object comprises a right rectangular prism and a right rectangular pyramid.Use the formula for the volume of a right rectangular prism. V= lwhV=(6.7)(2.9)(2.9)V= 56.347

Solution:

ThenUse the formula for the volume of a right rectangular pyramid.V= 1/3 lwhV= 1/3(6.7)(2.9)(2.1)V= 13.601Volume of the composite object is:56.347 + 13.601= 69.948The So, the volume of the composite object is approximately 69.9 m3.

Easy Right?That’s all in the chapter 1

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”!