# Question: Calculating Areas and Lengths of Circles with Different Radii

• Taylor_1989
In summary, two circles have a radius of 4 and 16 cm. The area of the circle with radius 4 is 16∏r^2 - ∏r^2 = (15∏r^2) and the area of the shaded ring is 16∏r^2 - ∏r^2 = (15∏r^2) + 2∏r. The total circumference is 10∏r.
Taylor_1989
I would just like to someone to have a quick look at my maths for this question. I do not feel 100% that I am doing it right.

Question: Two circles have a radii r cm and 4r cm.

Find in terms of ∏ and r
a) the area of the circle with radius 4r. Here are my working; by the way still can't get latex to work, I have tried to everything, could someone point me to a latex post to see where I am going wrong.

area = ∏*r^2 ====> ∏*(4r)^2 =====> (16∏r^2)

b) The area of the shaded ring:

area = 16∏r^2 - ∏r^2 = (15∏r^2)

c) The total length of the inner and outer edges of the shaded ring.

Circumference = 2∏r =====> 2∏4r ======> 8∏r =====> 8∏r + 2∏r = (10∏r)

The answers and the ones with brackets. I have attched a drawing of the image that goes with the question. Not sure if really needed.

#### Attachments

• physicsforums.jpg
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looks okay

Taylor_1989 said:
I would just like to someone to have a quick look at my maths for this question. I do not feel 100% that I am doing it right.

Question: Two circles have a radii r cm and 4r cm.

Find in terms of ∏ and r
a) the area of the circle with radius 4r. Here are my working; by the way still can't get latex to work, I have tried to everything, could someone point me to a latex post to see where I am going wrong.

area = ∏*r^2 ====> ∏*(4r)^2 =====> (16∏r^2)
Your use of ====> and =====> above is pretty much meaningless. Your work would be improved if you described better what you are doing and used = to connect expressions with the same value.

For example,
Area of inner circle = ## \pi r^2##
Area of outer circle = ## \pi (4r)^2 = 16\pi r^2##

The right sides of the equations above are written using LaTeX. Right-click on either of them to see what I wrote.
Taylor_1989 said:
b) The area of the shaded ring:

area = 16∏r^2 - ∏r^2 = (15∏r^2)

c) The total length of the inner and outer edges of the shaded ring.

Circumference = 2∏r =====> 2∏4r ======> 8∏r =====> 8∏r + 2∏r = (10∏r)
This would be better, IMO, as it gives the reader a better idea of what you are doing.
Total circumference = Circumference of outer circle + Circumference of inner circle
= ##2\pi (4r) + 2\pi r = 8\pi r + 2\pi r = 10\pi r##
Taylor_1989 said:
The answers and the ones with brackets. I have attched a drawing of the image that goes with the question. Not sure if really needed.

I have tried to put latex in, but have problems even when I write it in latex. I write the code, but it never changes to latex form. Do you have any suggestions why I have this problem?

You have to put it inside a pair of [noparse]$$and$$[/noparse] tags or a pair of [noparse]$and$[/noparse]. Alternatively you can use a pair of  tags (at start and end) or a pair of ## tags (at start and end).

Edit: It appears that [ noparse ] has stopped working. The first sentence above says

You have to put it inside a pair of [ tex] and [ /tex] tags or a pair of [ itex] and [ /itex]. (Omit the leading spaces.)

Last edited:
Thanks for the info, I was using [itex] as a tag to star and finish; maybe way it was not working.

## 1. What is a quick maths check for algebra?

A quick maths check for algebra is a method used to verify whether a given algebraic equation or expression is correct. It involves substituting values for the variables and simplifying the equation to see if the two sides are equal.

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To do a quick maths check for algebra, you can follow these steps:

1. Substitute values for the variables in the equation.
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