## Monday, December 17, 2012

### Textbook 1.3 Question 23

• Before I looked for the surface area I had to divided the side into a way I could find the surface area easily because the shape is irregular.
• So I divided the shape into two pieces one into a triangle and one into a rectangle.
• First I used the Pythagorean Theorem to find the measurement of the base of the pool.
• After I square rooted my answer that gave me the length of the base.
• Now I can find the surface area of that side.

• Now I started finding the surface area of the inside walls of the pool that need painting which was the bottom of the pool, the side, back and front.
• I found the surface area of the rectangle in the irregular shape then the triangle then added them together, then multiplied it by two.
• Then I found the S.A of the base (bottom of the pool) by multiplying the length and width.
• Next I found the front and the back by using the same formula but different heights because the pool gradually gets greater.
• Then as a result I added all the it together and got an answer of 389 m^2.
*This may not be the answer at the back because I could not find a way to get that answer. (:

### Chapter 1,3 Page 34: Question 17

Question: The hollow passages through which smoke and fumes escape in a chimney are called flues. Each flue shown is 2cm thick, 20 cm high, and has a square opening that is 20cm by 20 cm.

a) What are the outside dimensions of the two flues?
b) If the height of each flue is 30cm, what is the outside surface area of the two flues? Hint: Do not forget the flat edges at the top.

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#### SOLUTION

• Since each flue shown is 2cm thick, and the given opening is 20cm by 20cm, we know that it doesn't really give us the width of one flue.
• One flue will be 24cm because you are adding the 2cm from each side and adding the width from the given opening.
• Dimensions are width x height (24cm x 20cm)
• 20cm + 2(2cm) = 24cm
Answer: The outside dimensions of the two flues are 24cm(width) by 20cm(height).

• Before we start, to make it easier we should be able to change the image so it cooperates with the given description for the flue.
• Instead of 20cm, I changed it to 30cm. The length will be 24cm because I used the same method. [ 20cm + 2(2cm) ]
• However, for the width of the two flues together, it is 48cm because I doubled 24cm because there are two flues, not one.
SA= lw + 2( lh+hw ) - 2( lw )
= (24cm)(48cm) + 2 [ (24cm)(30cm) + (30cm)(48cm) ] - 2[(20cm)(20cm)
= 1152cm² + 2( 720cm² + 1440cm² ) - 2(400cm²)
= 1152cm² + 2(2160cm²) - 800cm²
= 1152cm² + 4320cmm² - 800cm²
= 5472cm² - 800cm²
= 4672cm²

Answer: The surface area of the two flues is 4672cm².

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### Textbook: Page 34 #14

14) A chimney has the dimensions shown. What is the outside surface area of the chimney? Give your answer to the nearest hundredth of a square metre.

Lables:
r1 & h1= big cylinder
r2 & h2= small cylinder

SA= 2π(r1xh1) + 2π(r2xh2) + [πr2^2 - πr1^2]
SA= 2π(25)(90) + 2π (15)(40) + [π(25)^2 - π(15)^2]
SA= 14137.17cm^2 + 3769.91cm^2 + [1963.50 - 706.86]
SA=  14137.17cm^2 + 3769.91cm^2 + 1256.64cm^2
SA= 19163.71cm^2

Conversion:
1963.71cm^2 x 1m^2/10000cm^2=1.92m^2

## Friday, December 14, 2012

### Textbook: Chapter 1.3 - Question #13

13) A mug for hot beverages is to be designed to keep its contents warm as long as possible.
The rate at which the beverage cools depends on the surface area of the container.
The larger the surface area of the mug, the quicker the liquid inside it will cool.

a) What is the Surface Area?
Assume that neither has a lid.

b) Which is the better mug for keeping drinks warm? Justify your answer.

SOLUTION:

To find the Surface Area of both mugs, we need to know what formula to use.
Since these look like CYLINDERS, we must use the formula for a cylinder.

Surface Area of a Cylinder = 2 π r² + 2 π r h

BUT.. there's a catch! In the question, they said assume that there is no lid.
SO.. since there are usually 2 circles in a cylinder, we must remove the area of 1 circle in the formula.
Our formula will change into:  π r² + 2 π r h

Here are my solutions: PART A

Blue Mug = 286.52 cm²
Red Mug = 298.64 cm²

PART B

The mug best for keeping drinks warm is the BLUE mug because in the question itself it stated "The larger the surface area of the mug, the quicker the liquid inside it will cool." The surface area of the blue mug is only 286.52 cm ² compared to the red mug that is 298.64 cm ²

### Textbook Page 34: Question 15

15.) Twila made the object shown

a.) How can you use symmetry to help find the surface area of this object?

The object's top and bottom faces, left and right faces, and front and back are symmetrical.

b.) What is the surface area?

## Wednesday, December 12, 2012

### December 11, 2012

Today we learned the formulas for finding the surface areas (S.A) of a:

1. Cube
2. Rectangular Prism
3. Pyramid
4. Cylinder
In order to find the surface area of a cube, use this formula:

S.A = 6 s²
(Where "s" is the measure of 1 edge.)
That means that to find the surface area of a cube, find the area of one face of the cube first. Then square that number (multiply it by itself), and multiply it by 6 and you have your final answer.

To find the surface area of a rectangular prism, do this:

S.A = 2B + Ph
(Where "B" is the area of the base formed by multiplying its length by its width. "P" is the perimeter of the base multiplied by "h", the height of the prism.

or.......

S.A = 2 (lw + lh + wh)
(Where "l" stands for length, "h" is height and "w" is width.)

Finding the surface area of a pyramid... :

S.A = B + ½ Ps
(Where "B" is the area of the base. "P" is the perimeter, "s" is the slant height.)

The surface area formula for a cylinder:

S.A = π r ² + 2 π rh

or......

S.A = 2 π r (r + h)
(Where "r" is radius and "h" is height.)

And lastly, for finding the surface area of an isosceles triangular prism:

S.A = 2 (bh/2) + 2 b2 h2 + B)
(Where "b" is the base of the triangle, "h" is the height of the triangle, "b2" the base of the rectangle, "h2" is the slant height of the rectangle, and "B" represents the base of the figure found by multiplying "b" by "b2"

(sorry I couldn't upload any pictures!)

## 5.) A round chocolate cake is cut into eighths. A marble cake of the same size is cut into sixths. if Paulo eats three slices of chocolate cake and five slices of marble cake, how much cake is left over.

Paulo eats three slices from the chocolate cake and five slices from the marble cake.

The chocolate cake will have five pieces out of eight left while the marble cake will have one piece left out of six.

*I'm not sure if I have to add both left overs together*

5/8 + 1/6=

15/24 + 4/24 = 19/24

### Rational Number Test - Question 10

10. A 1-L can of paint covers 12m(squared). Determine the maximum dimensions of a sqaure ceiling you could paint with 3 1/2 L of paint. Express your answer to the nearest hundredth of a metre.

x3.5
L    1   =  3.5
C   12      42
x3.5

L= litres              C= cans of paint

square root of 42= 6.48

The maximum dimensions of a sqaure ceiling you could paint is 6.48m by 6.48m.

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

A = area
P = perimeter
A = 43.75 cm

7 congruent squares
14 congruent squares = P

First divide the area of the shape by the number of congruent squares to get the area of one  square.
Find the square root of the area of one square to get the side length.
Multiply the side length of one square by the number of sides to get the perimeter.

Algebraic Way

The perimeter of the shape is 35 cm.

## Saturday, December 1, 2012

### Test: Rational Word Problem Question 2

Question:

Information you will need to answer the question:
You would have to convert 1.5 hours into minutes which is 90 minutes.
You would then divide 90 minutes by 10 minutes because 5.2°C is dropping every 10 minutes,

Solution 1:
Multiply how much the temperature drops by 9 to find the total of how much it drops all together.

Solution 2:
This is the grade 9 way.

Always write a sentence answer after a word problem.

### Test: Rational Word Problem Question 6

• First I had to find how many times does 1  3/4  goes into 15   1/4.
• I made this easier for myself by changing the fractions into decimals.
• Then I found out that 1.75 goes into 15.25, eight times.
• This is because 1.75 x 8 = 14 and if you were to multiply by a higher number, your answer will be longer than 15.25. For example 1.75 x 9 = 15.75.
• This now let's us know that 14.00 m of the plank is cut in equal pieces of 8.
• Now we have to find out how much of the plank is left over.
• We find the solution to this by subtracting the length of the plank which is 15.25 by 14.
• 15.25 - 14.00 = 1.25 m
• So there is 1.25 m left over of the wooden plank.

### Test on Rational Number Word Problems #3

3.  A rectangular room measures 9.2 m by 6.9 m. To cover the floor of the room, the homeowner chooses square tiles with an area of 529 cm^2. How many tiles would be needed to completely cover the floor?

You need 1200 tiles to completely cover the floor.