# The surface area of 2 spheres is a ratio of 64:729. What is the ratio of their radii?

Dec 12, 2017

8:27

#### Explanation:

The surface area of a sphere is given by $4 \pi {r}^{2}$

Let r1 be the radius of the first sphere, and r2 be the radius of the second.

The problem statement gives us:

$\frac{4 \pi \cdot r {1}^{2}}{4 \pi \cdot r {2}^{2}} = \frac{64}{729}$
...you can see that the $4 \pi$ terms cancel.

therefore:
$\frac{r {1}^{2}}{r {2}^{2}} = \frac{64}{729}$

Take the square root of everything you see:

$\frac{\sqrt{r {1}^{2}}}{\sqrt{r {2}^{2}}} = \frac{\sqrt{64}}{\sqrt{729}}$ giving:

$\frac{r 1}{r 2} = \frac{8}{27}$

GOOD LUCK