Fructum

Mar 2009
223
50
Birmingham, Alabama.
You are given a fructum. With a bottom radius of 12 and an upper radius of 9. The slant height of the fructum is 6. Calculate the volume of the fructum, leaving any radicals and pi in the answer.

Please show your steps guys, and thank you in advance.
 

earboth

MHF Hall of Honor
Jan 2006
5,854
2,553
Germany
You are given a fructum. With a bottom radius of 12 and an upper radius of 9. The slant height of the fructum is 6. Calculate the volume of the fructum, leaving any radicals and pi in the answer.

Please show your steps guys, and thank you in advance.
I really can't resist, sorry: This must be a very funny kind of plant which provides us with those fruits (Surprised)

... and now: Have a look here: Frustum - Wikipedia, the free encyclopedia
 
Mar 2009
223
50
Birmingham, Alabama.
the frustum I talk of is a frustum of a cone, not a frustum of a pyramid.
 
May 2010
43
3
Norman, OK
You are given a fructum. With a bottom radius of 12 and an upper radius of 9. The slant height of the fructum is 6. Calculate the volume of the fructum, leaving any radicals and pi in the answer.

Please show your steps guys, and thank you in advance.
Since the base has radius 12 and the top has radius 9, the angle the side makes with the vertical is 30 degrees. I'm assuming this is a frustum of a right circular cone, since, if it were at a slant, then the volume of the frustum would be the same by Cavalieri's Principal.

This angle being 30 implies that the height of the cone from which the frustum came is 12/(1/2) = 24. The volume of this originating cone is (1/3)(π·12²)·24 = 1152π. The volume of the apical (the cone above the frustum) is (1/3)(π·9²)·18 = 486π. Thus, the volume of the frustum is 1152π - 486π = 666π. (Obviously, a devilish calculation.)
 
Apr 2010
23
0
just extend the frustrum to a cone, and fine the area of the entire cone minus the area of the small cone.