Math Is Fun Forum

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Area of Squares

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Area of Squares

Can you please help me with #5 and #10?????

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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
so please help me

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.

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Area of Squares

Can you please help me with Q 10

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Area of Squares

Please fill in these gaps:

Q6 answer =

Q7 answer =

Q8 answer =

Q9 answer =

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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.

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Area of Squares

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Area of Squares

hi owenflo,

Thanks for supplying those answers.

Q6.  I agree with your answer

Q7. I agree with your answer.

Q8.  I agree with your answer.

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Area of Squares

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Area of Squares

Please help me!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Area of Squares

Q6
43.301????

right

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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.

So round off your answer.

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Area of Squares

my teacher said the overlap i calculated earlier is not 75

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Area of Squares

well what estimate should i try

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Area of Squares

You are 'in' the zee-f thread.  She asked all the questions you are asking and, if you read the whole thread properly, you get all the answers you need.

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Area of Squares

What is Q10?