Question

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

Answer 1

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?

Answer 2

formulas*

Answer 3

@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.

Answer 4

*me to be

Answer 5

it is simple, here is your substitution:

\[\Large \frac{{{V_1}}}{{{V_2}}} = \frac{{\frac{{4\pi }}{3}R_1^3}}{{\frac{{4\pi }}{3}R_2^3}} = {\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^3} = {\left( {\frac{3}{4}} \right)^3} = ...?\]

Answer 6

27/64

Answer 7

Pretty sure my calculations are right.

Answer 8

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

Answer 9

hello there dan :)

Answer 10

that's right!

Answer 11

Hey dan :)

Answer 12

correct! @Thatsodan