# Question #23b0f

Oct 21, 2015

This is a volume problem using a truncated cone .

#### Explanation:

If you invert the flower pot upside down, you get a truncated cone:

The solution to the problem is to find the volume of the outer cone then subtract the volume of the inner cone.

The difference between the two cones is the 3 inch thick uniform wall.

There is a formula for the volume of a truncated cone:

$V = \frac{1}{3} \pi h \left({r}_{1}^{2} + {r}_{2}^{2} + {r}_{1} \cdot {r}_{2}\right)$

Where, ${r}_{1} =$radius of bottom and ${r}_{2} =$radius of top

Volume of outer truncated cone:

$V = \frac{1}{3} \pi 12 \left({9}^{2} + {6}^{2} + 9 \cdot 6\right) = 2148.849375$ cu in

Volume of inner truncated cone (subtract the 3" wall from each dimension):

$V = \frac{1}{3} \pi 9 \left({6}^{2} + {3}^{2} + 6 \cdot 3\right) = 593.7610115$ cu in

Volume of material (one pot) :
$V = 2 , 148.849375 - 593.7610115 = 1555.0883635$ cu in

Finally, Volume of 1000 pots :

Answer $= 1000 \cdot 1555.0883635 = 1 , 555 , 088$ cu in
$\approx 900$ cubic feet of material

Hope that helped