December 6, 2012 Notes

Surface Area

       - Area is the number of the square units it takes to cover a surface. Always expressed as squared units.

Formulas for finding the area of a square, rectangle, triangle, and circle.

Finding the perimeter of a given area of a circle. 

    Question: A square has an area of 35 squared centimentres. What is the measure of its perimeter.

Find the area of the given shape.

First way: Finding the area of the whole shape including the missing shape.. Then subtract the area of the missing shape from the whole shape to get the area of the given shape.

Second Way: 

Test Question #9 Answers

Question: Close to the surface of the moon, the time a dropped object takes to fall to the surface can be calculated using the formula t= the square root of h/0.81. The time, t, is in seconds and the height, h, is in metres. If an object is dropped from a height of 250 m, how long does it take to reach the surface of the moon? Express your answer to the nearest tenth of a second. 

Math Test, Question # 1

Question:
A car uses fuel at a rate of 10.2 L/ 100 km while travelling at 90 km/h. At this rate of fuel consumption, how many litres of fuel would the car use if it travels 480 km? Express your answer to the nearest tenth of a litre.

This is how I solved this question:

My simple sentence answer:
The car will use 49.0 L of fuel if it travels 480 km.

Textbook Pg. 81 #31

Question: The area of a triangle can be determined using Heron's formula, which requires the side lengths of a triangle. Heron's formula is 

In the formula A is the area; a, b, and c are the side lengths; and s is half the perimeter or a+b+c/2. Determine the area of each triangle with the following side lengths. Express each area to the nearest tenth of a square centimetre. 

a) 15 cm, 12 cm, 10 cmb) 9.3 cm, 11.4 cm, 7.5 cm

The area of the triangle is 59.8 square cm.

b) 9.3 cm, 11.4 cm, 7.5 cm

The area of the triangle is 34.7 square cm. 

Rational Number Word Problems Test, Question 2 by Jay Jay

2. In a cold storage chamber, the temperature drops 5.2C every 10 minutes. If the temperature is initially 19C, what is the temperature in the chamber after 1½ hours?

Important things we know : 

5.2°C down every 10 minutes. (x9 = 90 minutes)

1½ hours  90 Minutes (90 ÷ 10 = 9)

Temperature is 19°C

19°C - (5.2°C x 9)    = 19°C - 46.8°C

                                  = -27.8°C

Therefore, the temperature in the cold storage chamber after 1½ hours is, -27.8°C

Math Test:Answering #4

4.The figure below is composed of seven congruent squares. The area is 43.75cm2. Calculate its perimeter.

A=Area
P=Perimeter

What We Know:
A=43.75cm2
7 congruent squares
P=14 congruent segments

Answer:
43.75cm2/7 =A of ONE square
                    =6.25cm2

square root of 6.25cm2=ONE side of small square
                                     =2.5cm

2.5cmx14=A of shape
                =35cm

Perimeter of the shape is 35cm.

Test Answer #7

Test Answers #10

 Question: 

          A 1-L can of paint covers 12m². Determine the maximum dimensions of a 

square ceiling you could paint with 3 1/2 L if paint. Express your answer to the 

nearest hundredth of a meter. 

Solution: 

            Hope this helps :)! Let's do better next test guys :D ! 

Symmetry

Symmetry

Definition of Symmetry:
When both sides are identical

Definition of Line of Symmetry
The line that divides the image into two identical shapes

The three lines of symmetry are:
- Horizontal 
- Vertical
- Oblique 

Transformation

is when a geometric shape moves.

These are the types of Tranformation:

- Rotation

- Translation

- Reflection

Translation- is when you move an object on a straight line.

It can be describe in;

- Words

- Abbreviated

- Symbols 

Symmetry

Define Symmetry :
is when the shape is reflected and becomes exactly image.

Define Line of Symmetry :
The line that divides the image in 2 identical halves.

The 3 types are:

1. Horizontal
2. Vertical
3. Oblique 

Example:

purple- horizontal

red- vertical

green and yellow- oblique

Red- vertical

Blue and purple- oblique

Green- horizontal

NO lines.

Transformation :

is when a geometric shape moves.

This can include:

1. reflection
2. translation
3. rotation

Translation- is when you move an object on a straight line.

It can be describe in;

- words

- abbreviated ( R4, D2 )

- symbols ( -->  , <-- )

Textbook pg 81 #34

Use the formula  r = √ A / π to determine the radius of a circular garden with an area of 40m². Express your answer to the nearest tenth of a metre. 

Textbook Pg 80 Question 24.c)

Question 24:

The distance, d, in kilometres, that a person can see across the ocean to the horizon is given by the formula d = square root of 12.74 x h. In the formula h is the height, in metres, of the person's eyes above the water. Calculate the distance that each of the following people can see across the horizon. Express each answer to the nearest tenth of a kilometre.

c) Yvonne is the pilot of an aircraft flying 5 km above the coastline.

Answer:

252.4 km is the distance that Yvonne can see across the horizon.

Textbook pg.81 #32

The answer is 35.7 cm 

Textbook pp. 80 Question 24.A) Ashton V.

                                                 Math Textbook pp. 80 Question 24.a







24. The distance , d, in kilometres, that a person can see across the ocean to the horizon is given by the formula d= the square root of of 12.74 x h. In the formula h= Height, in metres, of the person's eyes above the water. Calculate the distance that each of the folloeing people can see across the ocean to the horizon. Express each answer to the nearest tenth of a kilometre.

A) Adele is sitting on a lifeguard station at the edge of the ocean. Her eyes are 4.1m above the water.
--------------------------------------------------------------------------------------------------------------------------

that is how i found my awnser. ==>(Sorry if you can't read my writing)<==

The distance that Adele can see across the ocean to the horzion is 7.2 kilometres.

Textbook Page 80 Question #28

Question: The period, t, in seconds, of a pendulum is the time it take for a complete swing back and forth. The period can be calculated from the length, l, in metres, of the pendulum using the formula t = *square root* of 41. Determine the period of a pendulum with each of the following lengths. Express each answer to the nearest hundredth of a second. 

A) 1.6 m

l = 1.6 m
t = *square root* 4l 
t =  *square root* 4(1.6) 
t = *square root* 6.4 
t = 2.529

Round to nearest hundredth of a second: 2.53 s.

B) 2.5 m

l = 2.5 m
t = *square root* 4l 
t = *square root* 4(2.5)
t = *square root* 10
t = 3.1622 

Round to nearest hundredth of a second: 3.16 s.

C) 50 cm

l = 50 cm
t = *square root* 4l
t = *square root* 4(0.5)  << To get 0.5, you change 50 into a decimal, 50 divided by 100 gives you 0.5. 
t = *square root* 2
t = 1.414 

Round to nearest hundredth of a second: 1.41 s. 

Knowledge and Understanding

Explain why the solution to 2/5 x +3=1/2 is equivalent to the solution of 4x + 30 = 5

equation 1             equation 2
2/5 = 0.4                4
+3                          +30
1/2=0.5                  =5



equation 2 is equivalent to equation 1 because all the numbers for equation 2 are up one place value
the answer will always be the same throughout place values

x= -6.25

40x + 300 = 50 is equivalent to the other equations

                                  

Textbook Page 79 Question 16

Page 16.

a) The label on a 1-L can of paint states that the paint will cover an area of 10m squared. What is the side length of the largest square area that the paint will cover? Express your answer to the nearest hundreth of a metre.


 

 

The side length of the area that the paint will cover is 3.16 metres.

 

 

b) What is the side length of the largest square area that a 3.79-L can of the same paint will cover? Express your answer to the nearest hundreth of a metre.

 

 

 

 

 

 

 

 

 

 

 

 

The side length that a 3.79-L can of paint can cover is 6.16 metres.

 

 

c) Nadia is applying two coats of the paint to an area that is 4.6m by 4.6m. How much paint will she use if she applies the same amount of paint for each coat? Express your answer to the nearest tenth of litre. (SORRY ABOUT THE NECK BREAKER)

 

 

 

 

 

 

 

 

 

She will need 4.2 litres of paint for the two coats.

 

 

Textbook: Chapter 2.4 pg 81 Question #36

36. Determine √√√65536

-√65536 - perfect square because 256 x 256 = 65536

-√256 - perfect square because 16 x 16 = 256

-√16 - perfect square because 4 x 4 = 16

- The answer for √√√65536 is 4 because:

-Since there are three square root sign, you have to square root the given number three times.

~√√√65536

~√√256

~√16 = 4

 

Textbook question #35

The width of  a rectangle is 1/3 it's length. The Area of the rectangle 9.72 m2, what are the dimensions of the rectangle.

To do this question first you need to find the length of the rectangle. To get the length you can just compute the square root and then divide it by 1/3. 

  5.4 cm is the length of the rectangle now to find the width of the rectangle it says the the width is 1/3 the length so to get the width you just multiply 1/3 by 5.4cm and you will get the width.

5.4 x 1/3= 1.8cm  

The whole dimension of the rectangle is 1.8cm by 5.4cm

Page 79, Question 18 by Jay Jay Ladesma

18. A frame measures 30 cm by 20 cm. Can you mount a square picture with an area of 500 cm2 in the frame? Explain

No because the square root of 500 cm is 22.36068 therefore, each side of the picture is 22.36 cm and it is too big for the frame because it is only 30 cm by 20 cm.

Page 81, question number 31 A

V=square root

31. The area of a triangle can be determined using Heron's formula, which requires the side lengths of the triangle. Heron's formula is A=Vs(s-a)(s-b)(s-c). In the formula A is the area; a, b, and c are the side lengths; and s is half the perimeter or a+b+c/2.

     
Determine the area of each triangle with the following side lengths. Express each area to the nearest tenth of a square centimeter. 
A) 15cm, 12cm, 10cm
B) 9.3cm, 11.4cm, 7.5cm

A= Vs(s-a)(s-b)(s-c)
A= Area
a, b, c= side lengths 
S= Half of the perimeter 

15+12+10=37
=37/2
=18.5

 V 18.5(18.5-15)(18.5-12)(18.5-10)

 V 18.5(3.5)(6.5)(8.5) V 18.5(22.75)(8.5) V 18.5(193.375) V 3577.4375 =59.81168364If you round off 59.81168364 to the nearest tenth, it would be 59.8cm.


A) 15cm, 12cm, 10cm is the right answer.

Question 23

A rectangle floor that measures 3 m by 2 m covered by 384 square tiles. Determine the side length of each tile, in centimetres. State any assumptions you make.

3m = 300cm
2m = 200cm

l x w = A
300 x 200 = 60 000cm2
60 000cm2 / 384 = 156.25cm2

1 tile = 156.25cm2

√156.25cm2 = 12.5cm2

Each side length of the square is 12.5cm2
All 384 square tiles are 12.5cm2

Developing Proficiency Knowledge and Understanding

Solve for the variable

Math Textbook pg. 80 #27

Question :
The surface area of a cube is 100 cm2. Determine the edge length of the cube to the nearest tenth of a centimeter.


Answer:
100 cm2 = 10 000
10 000/6 = 1 666.6666....
√1 666.6666...= 40.8 cm2

40.8 cm2 = 1 664.64
1 664.64*6 = 9 987.84
√9 987.84 = 99.9 cm2 

The length of one edge of the cube is approx. 40.8 cm2

This  website helped me a lot with this question.