Question

The area of a circle is about 7 cm squared. By how many times will the area increase if the radius of the circle is tripled?

Answer 1

help please?(:

Answer 2

7 *3*3

Answer 3

hmmmm

Answer 4

explain further pleazz

Answer 5

i liked your help Hero

Answer 6

Okay, let me post the complete solution

Answer 7

Thank you

Answer 8

We know:

\[A = \pi r^2\]

We also know:

\[7 = \pi r^2\]

Now, we need to find the radius:

\[r = \sqrt{\frac{7}{\pi}}\]

Answer 9

Afterwards we need to multiply that by 3, and re-insert it into the area of a circle formula:

Answer 10

i dont quite understand how we find the radius

Answer 11

Do you know how to isolate r in the following equation \[7 = \pi r^2 \]?

Answer 12

you divide by pi right?

Answer 13

Okay, if you did that you would end up with

\[\frac{7}{\pi} = r^2\]

We have r^2, but we still need to isolate r

Answer 14

What can we do to both sides to isolate r?

Answer 15

so we square root it right?

Answer 16

Yes, and that is how we end up with

\[\sqrt{\frac{7}{\pi}} = r\]

Answer 17

oh isee..then from there what is our next step?

Answer 18

You found r, but we have to triple it. Once we triple it, we place it back into the area formula, then find the value of A

Answer 19

Notice that r can be re-written as:

\[\frac{\sqrt{7}}{\sqrt{\pi}}\]

Answer 20

Now we have to multiply this by 3

Answer 21

how do you multiply sumthin like that by 3?

Answer 22

When we do this we get:

\[r = \frac{3 \sqrt{7}}{\sqrt{\pi}}\]

Answer 23

Now we place that back into the area formula:


\[A = \pi (\frac{3 \sqrt{7}}{\sqrt{\pi}})^2\]

Answer 24

Amazingly, we get A = 63

Looks like @matricked shortcut worked

Answer 25

how dipe that last equation in the calculator?

Answer 26

not dipe but *type

Answer 27

Depends on what kind of calc you have. I have TI-Nspire, the only calc I would recommend

Answer 28

i have some sort od scientic one that can handle this but i dont get how to multiply out the radicals?

Answer 29

By the way the answer is not 63 cuz its not one of the options

Answer 30

What are the answer choices? Two people use two different methods and come up with the same answer. I'm pretty sure it is correct.

Answer 31

I performed every step correctly.

Answer 32

Reread the original problem question cuz I think yo guys forgot something. The answers are 1.5, 3, 6 and 9

Answer 33

Oh, I see. 63/7 = 9

Answer 34

It asked "by how much" does the area increase. It increased from 7 to 63

7 x 9 = 63, therefore it increased by a factor of 9

Answer 35

thank you i got it

Answer 36

yw

Answer 37

can u help me with a few more other problems? youe explain it very good

Answer 38

You assume I have time to explain every step