## anonymous one year ago The area of two sphere have the ratio 4:25. what is the ratio of the radii?

1. amistre64

how do you determine the area of a sphere?

2. anonymous

Sorry, but I don't know how ..

3. pooja195

$\huge~\rm~A=\pi~r^2$

4. anonymous

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

5. pooja195

@amistre64

6. anonymous

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

7. anonymous

area of surface of sphere=4 pi r^2

8. anonymous

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

9. anonymous

and then?

10. amistre64

if r^2 = 4 and R^2 = 25 what are the values of r and R ?

11. amistre64

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.

12. anonymous

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

13. anonymous

and the ratio is 2:5...

14. anonymous

thanks guys :)

15. anonymous

yw

16. anonymous

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