Question #23b0f

Question

1422 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-21T01:27:49

This is a volume problem using a truncated cone .

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

enter image source here

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:

$V = 1/3pih(r_1^2+r_2^2+r_1*r_2)$

Where, $r_1=$ radius of bottom and $r_2=$ radius of top

Volume of outer truncated cone:

$V = 1/3pi12(9^2+6^2+9*6)=2148.849375$ cu in

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

$V = 1/3pi9(6^2+3^2+6*3)=593.7610115$ cu in

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

Finally, Volume of 1000 pots :

Answer $=1000*1555.0883635=1,555,088$ cu in
$~~900$ cubic feet of material

Hope that helped