The diameter of a circle is tripled. How does this affect the area of the circle

Question

The diameter of a circle is tripled.  How does this affect the area of the circle

tkhunny · Answer

Just do it.  $Area = \pi r^{2} = \pi \left(\dfrac{d}{2}\right)^{2}$, right?

Now, in place of "$d$", put "$3d$" and see what happens.

anonymous · Answer

Ok
I'm in sixth grade can u make it easier please

anonymous · Answer

Please

tkhunny · Answer

No.  That's all there is to it.

Practice problems:

$3^{2} =\;??$

$(2f)^{2} =\;??$

tkhunny · Answer

It doesn't matter what grade you are in.  If you should not be given such a problem, why were you given this problem?  You must have been given SOME tools to solve it.

Did you talk in class about length, area, and volume and their relationships?  We have to find some way to figure out why it was reasonable for you to have this problem statement to solve.

anonymous · Answer

Ik that  pi =3.14
But like the question doesn't say what the original area is to the diameter or the radius
It just says:
The diameter of a circle is tripled.  How does this affect the area of the circle?

anonymous · Answer

Plz help me
My mom is terrible at math!!!!

johnweldon1993 · Answer

@Catierose02 Alright so we have a circle...

The area of a circle is equal to $\large \pi r^2$

r is equal to the radius of the circle...which is half of the diameter

|dw:1397170381617:dw|
|dw:1397170409617:dw|

johnweldon1993 · Answer

So if the area if $\large \pi r^2$

Lets choose a random Diameter....lets say 10

this means that the radius would be half that...and will be 5


Area of that will be
$$\large \pi 5^2 = 25 \pi$$

Okay....now say that we triple that same diameter....so instead of 10...we have 3 times 10 which is 30

That means the radius will now be half of 30....which is 15


Area of this new one
$$\large \pi 15^2 = 225 \pi$$

So we went from $\large 25\pi $ to $\large 225 \pi$

So what change is that?

anonymous · Answer

Ummmmm
200 squared units

johnweldon1993 · Answer

Not quite...we are thinking "How many times bigger is this new circle compared to the old circle?

So what is 225 / 25 ?

anonymous · Answer

9

johnweldon1993 · Answer

Correct...

so

If the diameter of a circle is tripled...how will it affect the area?"

Well it would make the area 9 times bigger

anonymous · Answer

Ooooooooooooooo
OMG THANK U SOOOOOO MUCH!

johnweldon1993 · Answer

No problem :)