## anonymous one year ago What is the ratio for the volumes of two similar spheres, given that the ratio of their radii is 3:4? A. 27:64 B. 16:9 C. 9:16 D. 64:27

1. Michele_Laino

the volume of the first sphere is: ${V_1} = \frac{{4\pi }}{3}R_1^3$ whereas the volume of the second sphere is: ${V_2} = \frac{{4\pi }}{3}R_2^3$ so if we divide side by side those formula each other, we get: $\frac{{{V_1}}}{{{V_2}}} = \frac{{\frac{{4\pi }}{3}R_1^3}}{{\frac{{4\pi }}{3}R_2^3}} = {\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^3}$ now, we have: $\frac{{{R_1}}}{{{R_2}}} = \frac{3}{4}$ so, please substitute that ratio into the expression for the ratio V_1/V_2, what do you get?

2. Michele_Laino

formulas*

3. anonymous

@Michele_Laino I'm sorry if you should find be to be incompetent, seeing as how well this was explained, but I do not understand what it is I should be substituting in.

4. anonymous

*me to be

5. Michele_Laino

it is simple, here is your substitution: $\Large \frac{{{V_1}}}{{{V_2}}} = \frac{{\frac{{4\pi }}{3}R_1^3}}{{\frac{{4\pi }}{3}R_2^3}} = {\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^3} = {\left( {\frac{3}{4}} \right)^3} = ...?$

6. anonymous

27/64

7. anonymous

Pretty sure my calculations are right.

8. anonymous

Yep, double checked. Thank you @Michele_Laino! :)

9. dan815

hello there dan :)

10. Michele_Laino

that's right!

11. anonymous

Hey dan :)

12. Michele_Laino

correct! @Thatsodan