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denis_gylaev

Member

Registered: 2015-03-19

Posts: 66

Circle Area Problems

In the figure with four circles below, let A_1 be the area of the smallest circle, let A_2 be the area of the region inside the second-smallest circle but outside the smallest circle, and so on. If A_1 : A_2 : A_3 : A_4 = 1 : 2 : 3 : 4, then find the ratio of the largest radius to the smallest radius.

Let A, B, C, be three points on a line such that AB = 2 and BC = 4. Semicircles are drawn with diameters \overline{AB}, \overline{AC}, and \overline{BC}. Find the area of the shaded region.

denis_gylaev

Member

Registered: 2015-03-19

Posts: 66

Re: Circle Area Problems

Another question: A sector of a circle has a central angle of 80 degrees. If the area of the sector is 32\pi, what is the radius of the circle?

I am getting 8 sqrt2 but this is wrong...

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Circle Area Problems

hi denis_gylaev

Q1.  the second smallest has area A1 + A2 = A1 + 2A1 = 3A1

You can continue this to get the largest area in terms of A1.

The ratio of the radii is the root of the ratio of the areas.

Q2.  The area of the semi circle on AC is half pi 9^2.

       ditto ...................................BC is half pi 2^2

       ditto ...................................AB is half pi 1^2

So you can get the shaded area  by subtraction and simplification.

Q3. 

Then make r^2 the subject (don't evaluate yet because it's a 'nice' square root)

Where did root 2 come from ?

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

denis_gylaev

Member

Registered: 2015-03-19

Posts: 66

Re: Circle Area Problems

Hi can I have a solution aswell?

I am getting 2pi for number 2

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Circle Area Problems

hi

Hi can I have a solution as well?

That's not how I help.  You have these choices:

Post an answer and I'll say if I think it is right.  Number 2 is right! 

Post what you can do before you get stuck and I'll help a bit more.

Post that you cannot even do a first step and I'll try to explain a bit better.

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

denis_gylaev

Member

Registered: 2015-03-19

Posts: 66

Re: Circle Area Problems

I am also getting 12 for nr 3

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Circle Area Problems

Not what I thought.  But I now think I have misunderstood what you wrote:

. If the area of the sector is 32\pi,

I thought you meant:

But maybe you meant:

If so, then 12 is correct.

Do you need more help with Q1 ?

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

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: Circle Area Problems

Another question: A sector of a circle has a central angle of 80 degrees. If the area of the sector is 32\pi, what is the radius of the circle?

I am getting 8 sqrt2 but this is wrong...

Hi denis_gylaev, you can write the π symbol if you type:

:pi

denis_gylaev

Member

Registered: 2015-03-19

Posts: 66

Re: Circle Area Problems

Ok I will clean up confusion, the sector is 32π

In the figure with four circles below, let A_1 be the area of the smallest circle, let A_2 be the area of the region inside the second-smallest circle but outside the smallest circle, and so on. If A_1 : A_2 : A_3 : A_4 = 1 : 2 : 3 : 4, then find the ratio of the largest radius to the smallest radius. Answer: sqrt{10}: 1

Let A, B, C, be three points on a line such that AB = 2 and BC = 4. Semicircles are drawn with diameters \overline{AB}, \overline{AC}, and \overline{BC}. Find the area of the shaded region. Answer: 2π

A sector of a circle has a central angle of 80 degrees. If the area of the sector is 32π, what is the radius of the circle? Answer: 12

Bob your hints are really nice
Please confirm my answers, sorry for the confusion thanks

Last edited by denis_gylaev (2015-09-06 06:05:27)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Circle Area Problems

I agree with all three answers.  Well done!

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