Volume

**Dragon** · October 24th 2006, 02:58 PM

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?

**topsquark** · October 24th 2006, 05:49 PM

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

Thread: Volume

LinkBack

Thread Tools

Display

Volume

Similar Math Help Forum Discussions

Comparison between cylinder volume and extruded circular spline volume equal dia

volume flux, mass flux and volume flo

[SOLVED] Theoretical Proof for volume of a cone in relation to the volume of a cylind

divergence = flux / volume is independant of the limiting volume

Volume

Search Tags