What is the perimeter....

[eddy2017]

the figure above is made by cutting a circular hole with a diameter of 10 inches out of a larger circle which has an area of 314 inches squared, then cutting the resultant figure in half. Both circles share a center.What is the perimeter of the figure above in inches.
Any hints ?.

 

[Steven G]

Given the area of the larger circle, can you find the radius of that circle?

A=pi*r^2, so r = sqrt(A/pi).

 

[nasi112]

Let [MATH]R[/MATH] be the radius of the larger circle and let [MATH]r[/MATH] be the radius of the small circle.

The perimeter of the given shape is

[MATH]\frac{2\pi R}{2} + \frac{2\pi r}{2} + 2R - 2r[/MATH]
Follow what Jomo did to find [MATH]R[/MATH].

 

[eddy2017]

Given the area of the larger circle, can you find the radius of that circle?

A=pi*r^2, so r = sqrt(A/pi).

Thanks to you both for replying. so radius would be equal to,
√r =√(314/3.140)
√r=√100
r=10
the radius of the larger circumference is 10

now I have to find the radius of the smaller circle. any hint for that?

 

[JeffM]

Thanks to you both for replying. so radius would be equal to,
√r =√(314/3.140)
√r=√100
r=10
the radius of the larger circumference is 10

Yes. So what is the circumference of HALF that outer circle?

 

[eddy2017]

Yes. So what is the circumference of HALF that outer circle?

should be 5 right. half of 10.

 

[JeffM]

What is the relationship between a circle’s radius and its circumference?

 

[eddy2017]

Let [MATH]R[/MATH] be the radius of the larger circle and let [MATH]r[/MATH] be the radius of the small circle.

The perimeter of the given shape is

[MATH]\frac{2\pi R}{2} + \frac{2\pi r}{2} + 2R - 2r[/MATH]
Follow what Jomo did to find [MATH]R[/MATH].

if I have the big radius and the small one then I can plug in the info I have in your formula right?
if I were to follow that formula would this be the right substitution of values?

p=2πR/2+2πR/2+2R-2rp=(2×3.14×10)/2+(2×3.14×10)/2+2(10)-2(5)

I assume that we divide by two here cos we have two circles and minus the radii

 

[eddy2017]

What is the relationship between a circle’s radius and its circumference?

the radius is half its diameter so
The circumference of a circle is equal to pi times the diameter. The diameter is two times the radius, so the equation for the circumference of a circle using the radius is two times pi times the radius.
I have also read this: Pi (Ratio of the Circumference of a Circle to Its Diameter) Circles are all similar, and "the circumference divided by the diameter" produces the same value regardless of their radius. This value is the ratio of the circumference of a circle to its diameter and is called π (Pi).

 

[JeffM]

Yes. So you have calculated the radius of the outer circle to be 10. So the circumference is what numerically? And therefore the circumference of half the outer circle is what numerically?

 

[Deleted member 4993]

if I have the big radius and the small one then I can plug in the info I have in your formula right?
if I were to follow that formula would this be the right substitution of values?

p=2πR/2+2πR/2+2R-2rp=(2×3.14×10)/2+(2×3.14×10)/2+2(10)-2(5)

I assume that we divide by two here cos we have two circles and minus the radii

No - the correct equation is:

p = 2πR/2+2πr/2+2R-2r ............................... note 'r' in the right-hand-side of the equation

Continue and finish the calculation....

 

[eddy2017]

No - the correct equation is:

p = 2πR/2+2πr/2+2R-2r ............................... note 'r' in the right-hand-side of the equation

Continue and finish the calculation....

31.4 + 15.7 + 20 -10
= 57.1 the perimeter of the figure is 57.1 inches

 

[eddy2017]

Yes. So you have calculated the radius of the outer circle to be 10. So the circumference is what numerically? And therefore the circumference of half the outer circle is what numerically?

following nasi's formula made it easy but I wanna try and answer your question.
you said 'So the circumference is what numerically.
I think I have been given the area of the circumference 314 in^2.
I think that is what the circumference is numerically to answer your question.

 

[nasi112]

31.4 + 15.7 + 20 -10
= 57.1 the perimeter of the figure is 57.1 inches

Bravo?

 

[eddy2017]

following nasi's formula made it easy but I wanna try and answer your question.
you said 'So the circumference is what numerically.
I think I have been given the area of the circumference 314 in^2.
I think that is what the circumference is numerically to answer your question.

 

[eddy2017]

but the problem is asking about the perimeter as there are two semicircles
so we add the major semicircle + minor semicircle to have the curved sides of the perimeter that they ask for.

 

[nasi112]

but the problem is asking about the perimeter as there are two semicircles
so we add the major semicircle + minor semicircle to have the curved sides of the perimeter that they ask for.

Besides major semicircle + minor semicircle perimeters, there are two straight lines perimeters [MATH]= 2R - 2r[/MATH]
If you ignore them, you will not have the complete perimeter they are asking for.

 

[eddy2017]

Besides major semicircle + minor semicircle perimeters, there are two straight lines perimeters [MATH]= 2R - 2r[/MATH]
If you ignore them, you will not have the complete perimeter they are asking for.

yes, you're right.

 

[eddy2017]

yes, you're right.

I have to ask this question cos it is not clear in my mind yet.
the diameter is said t0 be 10 inches, right?.
I am attaching a drawing where I draw the diameter is that correct?.
and if so, is there a quick way to find the length of the two straight lines that close the curves?
what I am not understanding well is why the big radius and a small one?. don't still get it clealry/

 

[lev888]

I have to ask this question cos it is not clear in my mind yet.
the diameter is said t0 be 10 inches, right?.
I am attaching a drawing where I draw the diameter is that correct?.
and if so, is there a quick way to find the length of the two straight lines that close the curves?

On the diameter line mark the center, small radius, large radius. This should answer your question.