more urgent areas and ratios

**sanee66** · July 22nd 2007, 12:58 PM

I do not understand most of these, Please help

**Jhevon** · July 22nd 2007, 01:13 PM

Originally Posted by sanee66

I do not understand most of these, Please help

To A

the area of the rhombus is $4 \times _{area} \triangle UMW$

to find the area of the triangle use the $\frac {1}{2} \cdot base \cdot height$ formula (note, you have to find the height, use Pythagoras' theorem

got it?

do you know what a rhombus is? do you know the properties of a rhombus? see here

questions become easier when you know what you are dealing with

**Jhevon** · July 22nd 2007, 01:45 PM

Originally Posted by sanee66

I do not understand most of these, Please help

B is $81 \sqrt {3}$

but i think that's what you meant to type... right?

double check question C. something is wrong with it

D is correct

clarify question E, what exactly is raised to the 4th power?

To F.

the circumference of a circle is given by:

$C = 2 \pi r$

For circle R, $12 \pi = 2 \pi r_R \implies \boxed { r_R = 6 }$

For circle S, $32 \pi = 2 \pi r_S \implies \boxed { r_S = 16 }$

Thus, the ratio of the radius of S to the radius of R is:

$r_S:r_R = \frac {r_S}{r_R} = \frac {16}{6} = \frac {8}{3} = 8:3$

**sanee66** · July 22nd 2007, 01:50 PM

Ratio of circumference of circle C to its radius is

. Which is the area of the circle?
Should be one of these

**Jhevon** · July 22nd 2007, 01:56 PM

Originally Posted by sanee66

Ratio of circumference of circle C to its radius is

. Which is the area of the circle?
Should be one of these

it seems you have some images missing, i can't see them. do you know how to use LaTex?

**sanee66** · July 22nd 2007, 02:12 PM

4pir4, I think the r is to the 4th and to the 6th for 16pir6.
I have no clue about latex and there are no images with the other question

Here is how it looks after finding the symbols
Area of circle P is 4πr4 and area of circle Q is16πr6. Which is the ratio of a radius of Q to a radius of P
The last 4 and the 6 are the powers and I think they go with the r.

**Jhevon** · July 22nd 2007, 02:14 PM

Originally Posted by sanee66

4pir4, I think the r is to the 4th and to the 6th for 16pir6.
I have no clue about latex and there are no images with the other question

Here is how it looks after finding the symbols
[FONT='Times New Roman','serif']Area of circle P is 4πr4 and area of circle Q is16πr6. Which is the ratio of a radius of Q to a radius of P[/font]

you could type, the first one for instance, as 4*pi*r^4

doing that avoids confusion.

**Jhevon** · July 22nd 2007, 02:23 PM

Originally Posted by sanee66

4pir4, I think the r is to the 4th and to the 6th for 16pir6.
I have no clue about latex and there are no images with the other question

Here is how it looks after finding the symbols
Area of circle P is 4πr4 and area of circle Q is16πr6. Which is the ratio of a radius of Q to a radius of P
The last 4 and the 6 are the powers and I think they go with the r.

here it is:

E

Recall that the area of a circle is given by $A = \pi r^2$

So, for P: $P_{area} = 4 \pi r^4$

$\Rightarrow 4 \pi r^4 = \pi r_P^2$

$\Rightarrow 4r^4 = r_P^2$

$\Rightarrow r_P = \sqrt {4 r^4} = 2r^2$

For Q: $Q_{area} = 16 \pi r^6$

$\Rightarrow 16 \pi r^6 = \pi r_Q^2$

$\Rightarrow 16r^6 = r_Q^2$

$\Rightarrow r_Q = \sqrt {16r^6} = 4r^3$

So the ratio of the radius of Q to the radius of P is:

$r_Q : r_P = \frac {r_Q}{r_P} = \frac {4r^3}{2r^2} = 2r$

**sanee66** · July 22nd 2007, 02:28 PM

I want to thank you so much for this. You are GREAT! That just leaves A and C and I have tried to get them. I don't have any images for C just what I posted and those are the answers I can choose from. I think when I am trying to use the P theorem, I am putting the numbers in the wrong place in the formula for A.

**Jhevon** · July 22nd 2007, 02:46 PM

Originally Posted by sanee66

I want to thank you so much for this. You are GREAT! That just leaves A and C and I have tried to get them. I don't have any images for C just what I posted and those are the answers I can choose from. I think when I am trying to use the P theorem, I am putting the numbers in the wrong place in the formula for A.

i will look over C again and see if i can decipher what you want to say.

to A

see the diagram below:

Pythagoras theorem says: If the sides of a right-triangle have lengths $a$ , $b$ and $c$ , (where $c$ is the hypotenuse), then the sides can be related as follows:

$a^2 + b^2 = c^2$

In the triangle below, $c = 14$ , $a = 10$ , we want to find $b$ which is $x$ on the diagram.

$a^2 + b^2 = c^2$

$\Rightarrow b^2 = c^2 - a^2$

$\Rightarrow b = \sqrt { c^2 - b^2 }$

$\Rightarrow b = x = \sqrt {14^2 - 10^2} = \sqrt {96}$

So the area of the triangle is:

$A = \frac {1}{2}bh = \frac {1}{2} 10 \cdot \sqrt {96} = 5 \sqrt {96}$

the area of the rhombus is 4 times the area of one triangle.

so area of rhombus is: $A_R = 4 \times 5 \sqrt {96} = 20 \sqrt {96} = 80 \sqrt {6}$

**Jhevon** · July 22nd 2007, 02:48 PM

the ratio of the circumference of ANY circle to it's radius is $2 \pi$ -- always. so your question simply makes no sense

**sanee66** · July 22nd 2007, 04:02 PM

The only answers I can choose for the answer to the area of the rhombus are
184.86
195.96
274.34
276.34

**Jhevon** · July 22nd 2007, 04:08 PM

Originally Posted by sanee66

The only answers I can choose for the answer to the area of the rhombus are
184.86
195.96
274.34
276.34

it is 195.96

that's the answer i gave you--or should be the answer, maybe i simplified incorrectly, let me check

EDIT: yeah, my mistake. i forgot the 20 that was multiplying the 4*sqrt(6), i corrected it. the answer is 80*sqrt(6) = 195.96

**sanee66** · July 22nd 2007, 04:38 PM

Ratio of circumference of circle C to its radius is 12pi. Which is the area of the circle? 36pi,34pi,28pi, or 24pi
I found a place that says
The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter.

is the ratio of the circumference of a circle to the diameter. Thus, for any circle, if you divide the circumference by the diameter, you get a value close to

.
C=2*pi*r
So 12pi=2*pi*r
Then what?

**Jhevon** · July 22nd 2007, 04:41 PM

Originally Posted by sanee66

Ratio of circumference of circle C to its radius is 12pi. Which is the area of the circle? 36pi,34pi,28pi, or 24pi
I found a place that says
The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter.

is the ratio of the circumference of a circle to the diameter. Thus, for any circle, if you divide the circumference by the diameter, you get a value close to

.
C=2*pi*r
So 12pi=2*pi*r
Then what?

ratio means divide, not equate. the ratio of a circumference of a circle to it's radius is $\frac {2 \pi r}{r} = 2 \pi$ always, $2 \pi$ cannot equal $12 \pi$ no matter what. so your question is off

Thread: more urgent areas and ratios

LinkBack

Thread Tools

Display

more urgent areas and ratios

Similar Math Help Forum Discussions

Ratios of areas

Ratios of Areas Help

Investigating ratios of areas and volumes

Ratios of areas of triangles..

4 urgent circumference and areas

Search Tags