Volume

Quote:

Originally Posted by Dragon

Suppose that eh volume of a ball is equal to Pie/6 times the volume of a cube What is the ration of the surface area of the ball to that of the cube?

I must be in a crabby mood tonight.

Pet peeve warning!!

It's spelled "pi" not "pie."

Pet peeve over. :)

Okay. We know that $V_b = \frac{ \pi }{6} \cdot V_c$ .

We also know that
$V_b = \frac{4}{3} \pi r^3$
$V_c = s^3$
$S_b = 4 \pi r^2$
$S_c = 6s^2$
(Where "s" is the side of the cube.)

So, solve $V_b$ for r:

$r = \left ( \frac{3}{4 \pi}V_b \right ) ^{1/3}$

So
$S_b = 4 \pi \left ( \frac{3}{4 \pi}V_b \right ) ^{2/3}$

Sim: $S_c = 6 \left ( V_c \right ) ^{2/3}$

Now sub in the relation for $V_b$ into the $S_b$ equation and take the ratio.

-Dan