Question

the ratio of the surface area of two spheres is 3:2. the volume of the larger sphere 2,916 in^3. what is the volume of the smaller sphere?

Answer 1

R^2:r^2 = 3:2

r = sqrt(2/3) R

4/3 pi r^3 = 4/3 pi R^3 (sqrt(2/3))^3 = 2,916 x (sqrt(2/3))^3

Answer 2

so whats the answer? cause this makes no since to me at all.... sorry

Answer 3

R is radius of big sphere.
r is radius of small sphere.
\[surface\ area = 4\pi \cdot r^2\]
\[\therefore {\cancel{4\pi} \cdot R^2 \over \cancel{4\pi} \cdot r^2}= \frac32\]\[\implies r^2 = \frac23 R^2\]\[\implies \large r = \sqrt \frac 23 \cdot R\]

Answer 4

\[\Large r=\left( \frac 23 \right)^\frac12R\]

\[volume\ of\ smaller\ sphere= \frac 43 \pi r^3\] replacing r using the previous formula
\[\Large = \frac 43 \pi \left[ \left( \frac 23 \right)^\frac12R\right]^3\]\[\Large = \frac 43 \pi R^3 \left( \frac 23 \right)^\frac32\]

Answer 5

Now,\[\frac 43 \pi R^3 = volume\ of\ larger\ sphere =2,916 in^3\]
\[volume\ of\ smaller\ sphere= \huge2916 \times \left( \frac23 \right)^\frac32inch^3\]
http://lmgtfy.com/?q=2916*(2%2F3)%5E(3%2F2)