Question

The area of two sphere have the ratio 4:25. what is the ratio of the radii?

Answer 1

how do you determine the area of a sphere?

Answer 2

Sorry, but I don't know how ..

Answer 3

\[\huge~\rm~A=\pi~r^2\]

Answer 4

oh wait can i use the formula for sa surface area of the sphere?

Answer 5

@amistre64

Answer 6

4(4piR^2)=25(4piR^2) like this?

Answer 7

area of surface of sphere=4 pi r^2

Answer 8

\[\frac{ 4 \pi r^2 }{ 4 \pi R^2 }=\frac{ 4 }{ 25 }\]
\[\frac{ r }{ R }=?\]

Answer 9

and then?

Answer 10

if r^2 = 4
and R^2 = 25

what are the values of r and R ?

Answer 11

as far as ratios go, there is a property:

quadratics are the square of linears

radius is a linear measure, area is a quadratic measure.

Answer 12

\[\frac{ r^2 }{ R^2 }=\frac{ 4 }{ 25 },\frac{ r }{ R }=\sqrt{\frac{ 4 }{ 25 }}=?\]

Answer 13

and the ratio is 2:5...

Answer 14

thanks guys :)

Answer 15

yw

Answer 16

I did not realize that I can cancel the 4 pi and squared both sides haha