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anonymous 5 years ago can somebody help me with ration please

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1. anonymous

be rational! ;)

2. anonymous

The celestial sphere shown at right has radius 9 inches. The planet in the sphere’s center has radius 3 inches. What is the ratio of the volume of the planet to the volume of the celestial sphere? What is the ratio of the surface area of the planet to the surface area of the celestial sphere?

3. anonymous

So you'll need to put the surface area of the one, over the other, and same for volume. I'm assuming you have/know the formula for the surface area or volume of a sphere..

4. anonymous

you mean 4/3pi3 right

5. anonymous

$V = \frac{4}{3}\pi r^3$ $A = 4\pi r^2$

6. anonymous

So the ratios will be $\frac{V_3}{V_9} \text{ and } \frac{A_3}{A_9}$

7. anonymous

for 9 is 972pi and 324pi and for 3 36pi and 36pi

8. anonymous

You need to divide them

9. anonymous

show me how..

10. anonymous

$Ratio_{volume} = \frac{324\pi}{972\pi}$

11. anonymous

i got 0.33333333333

12. anonymous

Hrm.. I think your original numbers are problematic... You should have.. $\frac{\frac{4}{3}\pi 3^3}{\frac{4}{3}\pi 9^3} = \frac{3^3}{(3^2)^3} = \frac{3^3}{3^6} = \frac{1}{3^3} = \frac{1}{27}$

13. anonymous

so that mean 1:3

14. anonymous

no that means 1:27

15. anonymous

for volume or SA

16. anonymous

that was for volume

17. anonymous

but now i need ratio for SA

18. anonymous

so do the same thing

19. anonymous

but with the surface area formula

20. anonymous

324 and 36

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