Circle. Yeah!

Lol nice pic!

So, area of a circle is $\pi r^2$ .

Increasing by 100% is doubling. So, if we double our $r$ , our area will quadruple:

$\pi (2r)^2=\boxed{4\pi r^2}$

And quadruple, in terms of increased by , will be $300$ %.

Why?

Because increase by simply tells us to take whatever we have and add that percentage of it to it. So for example, if you ave 100$, and you want to increase it by 50%, you'd simply add 50% of it to it:; 100$ + 50$ = 150$.

And we have a general pattern: if something increases $X$ times, it increases by $(X-1)100$ %.

yeah

Original radius = $r$

Increase in radius = $r\times$ 100% = $r$

New radius = $r$ + $r$ = $2r$

Original area = $\pi r^2$

New area = $\pi (2r)^2$ = $4 \pi r^2$

Percent increase in area = $\frac{(4 \pi r^2 - \pi r^2)}{\pi r^2}$ $\times$ 100% = 300%

To well understand this question, we can apply using 1 as example. A circle with 1 of radius, the area is π x r². Now increasing 100%, the radius is 2 and the area will increase by 4x. And to increase 4x, you need 300% because 1 + 3 = 4. Simple.

Original radius is r. Double radius is 2r. Area of circle is pi rsquared. If radius is 1 then 1+1=2 2 squared = 4. 100%+x=400% thus x=300%.

It is fairly easy to work put by eye. Imagine the small circle in the middle of the big circle and then look at the area of the big circle that is not covered by the small circle, this is the increase in size. Split the increase into quarters, and each quarter clearly wouldn't fill the area of the small circle. Split it in half and it would more than fill the small circle. Therefore thirds looks about right so the increase is equivalent to three times the area of the small circle. So the answer is 300%

Let area of original circle be r, area will be π r^2 . Now the radius is increased by 100% which means its doubled, so now radius is 2r, then area = π (2r)^2 =4 x π r^2 So the area becomes four times, but the answer wont be 400% because its asking for % increase in area, which will be (400-100)% = 300%

Or which easier way is just to think of thr radius being multiplied by Pi which is about 3

Let Radius of the circle be x Since it increases by 100% so the new radius will be x + x = 2x Consequently, the new area would be 4xx The old area is xx Now we can rush and say the answer is 400%, but wait, the question isn't asking for the ratio of the new area to the old area, it asks for the amount by which the area increases. To find it, we subtract the old area from the new area, 4xx - xx = 3xx, so the amount of increase is 300%

Increased by 100% means doubling the length of radius. And since the shape is kept the same (perfect circle), we can just solve the area ratio using dimension.

Length: R : 2R = 1:2 100% increase Area: R^2 : (2R)^2 = 1:4 300% increase.

We can do similarly to 3d volume, 4th or more dimensions.

Volume: R^3 : (2R)^3 = 1:8 700% increase.

It just seemed three times larger.

I just figured, 3.14 is closer to 300% than 400% and chose the answer based off of that

whaaaat........ lev 3 for this? its level1.

Lol, I guessed again.