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#126 2015-08-03 06:46:41

owenflo
Member
Registered: 2014-07-21
Posts: 115

Re: Area of Squares

What is the unit of measure for #1-4??????

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#127 2015-08-03 19:45:27

bob bundy
Registered: 2010-06-20
Posts: 8,354

Re: Area of Squares

hi owenflo,

Do you mean these questions?

I have a pizza. The radius is 10 inches long. The pizza was cut into 16 equal slices. When 1 slice was left, my sister and I both wanted it, so we agreed to cut it in half, but I like the crust more than she does, so we decided to cut it the "other way." In other words, the two pieces would not be symmetrical. The inside piece would contain all topping, and the outer piece would contain some topping and some crust.

1. Find the area of the whole pizza.

2. What is the area of one piece of pizza?

3. What is the area of a half-piece?

4. What would the area of the whole pizza be if it were made of half pieces?

The lengths are inches so the areas will be square inches or in.²

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#128 2015-08-04 13:13:03

owenflo
Member
Registered: 2014-07-21
Posts: 115

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#129 2015-08-04 19:00:21

bob bundy
Registered: 2010-06-20
Posts: 8,354

Re: Area of Squares

The area of a large sector (red area + yellow) is

where R is the large radius

and for the yellow area on its own

where r is the small radius.

If red = yellow

You have been told R so you can work out r from this.

Q10.  In order to do this part you must have already done Q6, Q7, Q8, and Q9.

What answers have you got for these?

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#130 2015-08-05 05:35:16

owenflo
Member
Registered: 2014-07-21
Posts: 115

Re: Area of Squares

My teacher is just waiting for question 10... I keep getting it wrong.

Q10

I sent
3/4+1/4=4/4

50^2+30^2=80^2

4/4*80^2*PI= 6400 PI

and she said I am not following your work here fully explain

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#131 2015-08-05 12:23:54

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Area of Squares

50^2+30^2=80^2

Of course, that is not correct.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#132 2015-08-05 16:44:21

owenflo
Member
Registered: 2014-07-21
Posts: 115

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#133 2015-08-05 18:48:41

bob bundy
Registered: 2010-06-20
Posts: 8,354

Re: Area of Squares

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#134 2015-08-06 04:08:35

owenflo
Member
Registered: 2014-07-21
Posts: 115

Re: Area of Squares

Q6
3/4 of the area

3/4 * 50^2 * pi= 1875 PI

Q7
1/4*30^2*PI

1/4*900*PI

225(PI)=706.858

Q8
1/4*30^2*PI

1/4*900*PI

225(PI)= 706.858

Q9
3/4*10^2*PI

3/4*100*PI

75(PI)

area 75, looks like it almost makes a square shape.

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#135 2015-08-06 04:18:02

owenflo
Member
Registered: 2014-07-21
Posts: 115

Re: Area of Squares

10. What is the total grazing area the goat can reach?

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#136 2015-08-06 05:49:18

bob bundy
Registered: 2010-06-20
Posts: 8,354

Re: Area of Squares

hi owenflo,

Q9  You don't need to calculate any more fractions of circles because the areas are already overlapping and the goat cannot eat the same grass twice.

The overlap is indeed roughly one square (that's 10 by 10 on this scale).  You can certainly use 75 as this is only an approximation.

Here's my diagram again.

The yellow region is for Q6.

The red and green are for Q7 and 8.

You have identified a good approximation for the area that has been counted twice.

Finally you can put it all together:

Q10 add Q6 + Q7  + Q8 and subtract Q9 so you only count this bit once.

That should give you a good approximate answer, which is what they want.  To get the exact answer would require higher maths such as calculus.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#137 2015-08-06 17:14:04

owenflo
Member
Registered: 2014-07-21
Posts: 115

Re: Area of Squares

i got the answer of 3213.716
???? is that correct

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#138 2015-08-06 19:37:46

bob bundy
Registered: 2010-06-20
Posts: 8,354

Re: Area of Squares

Sorry, but no.  Did you remember to multiply by pi ?

1875 x pi is more than that on its own.

If you post the decimal answer to each part I'll check them for you.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#139 2015-08-07 17:25:58

owenflo
Member
Registered: 2014-07-21
Posts: 115

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#140 2015-08-07 19:12:02

bob bundy
Registered: 2010-06-20
Posts: 8,354

Re: Area of Squares

Q6
1875 PI= ???

Q7

225(PI)=706.858  OK

Q8

225(PI)= 706.858

Q9

area = 75

Q10             = ??? + 706.858 + 706.858 - 75 =

B

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#141 2015-08-08 03:16:05

owenflo
Member
Registered: 2014-07-21
Posts: 115

Q6
43.301????

right

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#142 2015-08-08 03:17:26

owenflo
Member
Registered: 2014-07-21
Posts: 115

Re: Area of Squares

1875 PI is 5890.486

5890.486225+706.858+706.858-75= 7229.312

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#143 2015-08-08 07:01:31

bob bundy
Registered: 2010-06-20
Posts: 8,354

Re: Area of Squares

That looks like a reasonable answer .... but you need to round it off.

How accurate do you think you can be or need to be ?
The rope will not not be exactly 50 feet.
The barn will not be exactly 20 by 20.
Have you allowed for the knot in the rope or the goat being able to reach slightly further as its teeth can get further forward than its neck.

And how much does it matter ? The goat might leave one bit of grass as it doesn't look appetising enough.

And you have made an estimate for one area.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#144 2015-08-08 10:01:20

owenflo
Member
Registered: 2014-07-21
Posts: 115

Re: Area of Squares

my teacher said the overlap i calculated earlier is not 75

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#145 2015-08-08 18:58:23

bob bundy
Registered: 2010-06-20
Posts: 8,354

Re: Area of Squares

I'm sorry to hear that.

Look at post 102.  75 is a bit low.  I am happy to accept your value, as the rounding should only be to the nearest 100 anyway.  If you imagine that square divided into 4, then it should be clear that the white bit is a lot less than 25.  So try a larger value.  Hopefully, your teacher will accept your second answer.  You could point out that any answer that rounds to 7200 is satisfactory for the reasons I gave in my last post.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#146 2015-08-09 10:55:08

owenflo
Member
Registered: 2014-07-21
Posts: 115

Re: Area of Squares

I really dont understand what you or my teacher are saying, please explain.

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#147 2015-08-09 19:14:47

bob bundy
Registered: 2010-06-20
Posts: 8,354

Re: Area of Squares

In my diagram the scale is 10 feet for each square.

Q7 and Q8 ask you to calculate the area of a quarter circle (=quadrant).  These quadrants overlap as shown below.  So when you add 706.8 and 706.8 you are counting this overlap twice.

So you are asked to estimate the area of the overlap and subtract it from the total.

You have said it is 75 square feet.

I have split the square into four quarters.  Each quarter will have an area of 25.

The overlap (black area) = 100 - <the bits outside both green lines in my diagram>

Your teacher thinks 75 is too small.  The diagram shows why.  So you need to try a bigger estimate (between 75 and 100)

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#148 2015-08-10 08:02:46

owenflo
Member
Registered: 2014-07-21
Posts: 115

Re: Area of Squares

well what estimate should i try

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#149 2015-08-10 19:49:55

bob bundy
Registered: 2010-06-20
Posts: 8,354

Re: Area of Squares

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#150 2015-08-12 09:53:38

owenflo
Member
Registered: 2014-07-21
Posts: 115

What is Q10?

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