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

tips?

Answer 2

Surface area is proportional to the square of the radius, so if the surface area is 9 times...

Answer 3

hmmm

Answer 4

so

Answer 5

ehh

Answer 6

we need to find the area of the radius, right?

Answer 7

No...... How can you find the area of radius.....

Answer 8

true

Answer 9

Area of the radius? lolwut?

Answer 10

wait

Answer 11

I meant square of the radius

Answer 12

3 times 3, 1 times 1, 2 times 2, that type of area

Answer 13

I'm not sure if I get what you're saying.

Suppose \(A\) is the area of the first sphere, and \(A'\) the area of the second sphere. Likewise, \(r,r'\) are the radii for the first and second sphere respectively. Then\[\frac{A'}{A}=\left(\frac{r'}{r}\right)^2\]You have that \[\frac{A'}{A}=9\]So that means that \[\frac{r'}{r}=...?\]

Answer 14

ehh

Answer 15

the surface area of a sphere is 4/3 pi cubed, right?

Answer 16

j

Answer 17

k

Answer 18

ehh

Answer 19

\(4\pi r^2\), but we don't need that.

Answer 20

ahh

Answer 21

well

Answer 22

lets said that the original surface area was 81

Answer 23

when you multiply it by 9, it becomes 729

Answer 24

the radius obviously got bigger

Answer 25

If we let \(x=\frac{r'}{r}\), then can you more easily solve for \(x\) in this equation? \[9=x^2?\]

Answer 26

3=x

Answer 27

so the radius got three times bigger?

Answer 28

ahh

Answer 29

r to the ninth/ r to the first

Answer 30

dimensions

Answer 31

r to the third/ r to the first

Answer 32

Substituting back in, and solving, we get \[3r=r'\]So yes, it got 3 times bigger.

Answer 33

k

Answer 34

next problem

Answer 35

For similar figures,
\[(\frac{s_1}{s_2})^2 = \frac{A_1}{A_2}\]\[(\frac{s_1}{s_2})^3 = \frac{V_1}{V_2}\]