Question

If a spherical ball is enlarged so that its surface area is 9 times greater than its original surface area, then the original radius was multiplied by _________.

Answer 1

Surface area is 4pir^3, so for the total to be enlarged by a factor of 9, the radius must go from r^3=1 to r^3=9, so the radius was multiplied by the cube root of 9.

Answer 2

\(4\pi r^2 \implies \) the original radius was multiplied by 3 times.

Answer 3

did you understand the explanations?

Answer 4

Sorry i just got back from eating o.o

Answer 5

good to have "food for thought" :)

Answer 6

yes and water xD

Answer 7

one says 9 the other says 3 o.o

Answer 8

ok, lets call the radius of the smaller sphere \(r_s\) and the radius of the bigger sphere \(r_b\). then their surface areas would be:\[S_s=4\pi r_s^2\]and:\[S_b=4\pi r_b^2\]agreed?

Answer 9

Answerthisnow: do you know the surface area formula?

Answer 10

ya

Answer 11

surface area for what?

Answer 12

lol

Answer 13

ok, so now if we take their ratios we get:\[\frac{S_b}{S_s}=\frac{4\pi r_b^2}{4\pi r_s^2}=\frac{r_b^2}{r_s^2}=(\frac{r_b}{r_s})^2\]agreed?

Answer 14

FFM: your brain is never foolish - its you who are foolish! :)

Answer 15

lolol alright so the answer is 9? my brain is half melted....

Answer 16

I was right. It is 3 indeed.

Answer 17

opps my brain broke for a second there sorry

Answer 18

Answerthisnow: do you agree with the ration formula I typed above?

Answer 19

*ratio

Answer 20

Yes you are right asnaseer, I should stop second guessing myself :P

Answer 21

yeah :)

Answer 22

i.e. we have shown that:\[\frac{S_b}{S_s}=(\frac{r_b}{r_s})^2\]

Answer 23

ok, so now we just take square roots of both sides to get:\[\sqrt{\frac{S_b}{S_s}}=\frac{r_b}{r_s}\]

Answer 24

and you are told that:\[\frac{S_b}{S_s}=9\]

Answer 25

so the answer is?

Answer 26

\[\frac{r_b}{r_s}=\sqrt{\frac{S_b}{S_s}}=\sqrt{9}=?\]

Answer 27

3

Answer 28

bingo!

Answer 29

Is there a short way of doing stuff like this? I have 50 question to go xDD well tecnically i have 110 to go

Answer 30

there is a general rule which says:

1. the ratio of areas is equal to the square of the ratio of lengths
2. the ratio of volumes is equal to the cube of the ratio of lengths

but these can be derived as I did above.

Answer 31

Ok. Can i ask another here or should i just make another question thingy

Answer 32

Short way: Take the positive square root.

Answer 33

you should really post a new question "thingy" :)

Answer 34

kk xD i will thanks for the help

Answer 35

yw