Math Is Fun Forum

Irene

Member

Registered: 2024-04-22

Posts: 85

Area of plane shapes

Find the area of this rings. Take pi as 22/7. (a) outside diameter=8m and inside diameter=6m. Thanks (:

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I love Maths

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Area of plane shapes

The forumula for the area of a circle, radius r is

We are told diameters so we need to divide by 2 to get the right radius.  ie 4 and 3

If a ring is a circle with a hole in it you can get the area of the ring by calculating the area of the big circle and subtracting the area of the inside hole.

You're told to take pi as 22/7 which suggests to me there's a simplification in the working involving cancelling that 7.  Let's see:

pi is a common factor so you can do the subtraction and times the answer by pi

Bob

ps.  This example uses substitution into a formula, factorising and cancelling fractions.  Would you like some easier examples of any of these?

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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

Irene

Member

Registered: 2024-04-22

Posts: 85

Re: Area of plane shapes

Thanks again Bob. According to my workings, i got 88m. This is my workings: outside=8m, inside=6m =(8m+6m)(8m-6m) = 22/7×14m×2m=44×2=88m

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I love Maths

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Area of plane shapes

I got that too, at first. Then I re-read the question!

outside diameter=8m and inside diameter=6m.

The area formula needs the radius not the diameter. So you have to half the numbers given.  Here's another way to think about it.

Take that 8m circle.  You could box it in with a 8m by 8m square and that would have an area of 8x8 = 64.  So the answer must be a lot less than that.

Bob

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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

Irene

Member

Registered: 2024-04-22

Posts: 85

Re: Area of plane shapes

Okay, i will try solving it again.

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I love Maths

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 239

Re: Area of plane shapes

Thanks again Bob. According to my workings, i got 88m. This is my workings: outside=8m, inside=6m =(8m+6m)(8m-6m) = 22/7×14m×2m=44×2=88m

Although you used the diameters instead of radiuses, I noticed you used the identity:
a^2 - b^2 = (a+b)*(a-b)
This is a clever step that usually helps to simplify the calculation.
I think you will be very good in math.

Kerim

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Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

Irene

Member

Registered: 2024-04-22

Posts: 85

Re: Area of plane shapes

Thanks again Bob. According to my workings, i got 88m. This is my workings: outside=8m, inside=6m =(8m+6m)(8m-6m) = 22/7×14m×2m=44×2=88m

Although you used the diameters instead of radiuses, I noticed you used the identity:
a^2 - b^2 = (a+b)*(a-b)
This is a clever step that usually helps to simplify the calculation.
I think you will be very good in math.

Kerim

Thanks. But am still learning. Thats why there is MIF.

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I love Maths

paulb203

Member

Registered: 2023-02-24

Posts: 311

Re: Area of plane shapes

I found out from MIF that the name of this shape is an annulus (the area between two concentric circles).

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Prioritise. Persevere. No pain, no gain.

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 239

Re: Area of plane shapes

But am still learning.

Even at age 75, I am still learning. I am also making many mistakes before I solve the problems I am interested in.
I simply don't give up whenever I face a well-defined math problem (usually related to my designs).

On the other hand, having no interest in doing something has no remedy at all, even in the case of the most intelligent humans.

But I am afraid that the crucial starting point is self-trust. In other words, the unlimited power of the human's brain is limited by its owner only and to how far he believes it can help him. Unlimited/Limited trust results unlimited/limited intelligence (this is the practical meaning of the greatest advice said 2000 years ago).

Kerim

Last edited by KerimF (2024-07-02 01:11:57)

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Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.