volume of a rectangular prism whose dimensions are in the ratio 4:6:8 if the radius of the circumscribing sphere is 6sqrt of 29 inches

Question

anonymous · Answer

@triciaal

triciaal · Answer

@wolf1728  do you mind taking this?

wolf1728 · Answer

the radius is 6 * sq root (29 inches) OR 
6 * 5.3851648071 =
the radius = 32.3109888428

anonymous · Answer

yup, V=4/3 pi (6sqrt of 29)^3

anonymous · Answer

i got 141299.09 as the volume of sphere

anonymous · Answer

@wolf1728

anonymous · Answer

@dan815  @satellite73

wolf1728 · Answer

Yes I also get volume = 141,299.087528868
but we need the dimensions of the rectangular prism right?

anonymous · Answer

do you have an idea on how to solve this?.... im trying so hard to get it D:

wolf1728 · Answer

I'm searching the Internet to see how to do it.

anonymous · Answer

yup, ive done too and i cant find D:

wolf1728 · Answer

It seems I found a solution here: http://www.algebra.com/algebra/homework/Volume/Volume.faq.question.110359.html They say a properly positioned rectangular prism will have a diagonal that is the diameter of the sphere. So, we know the diagonal should be the sphere's diameter or 64.6219776856

anonymous · Answer

its circumscribe

wolf1728 · Answer

The diagonal of the prism = the circumscribed sphere's diameter

triciaal · Answer

@wolf can you sketch the picture of the sphere with the prism?

anonymous · Answer

2sqrt of 29 is the diagonal of the prism

anonymous · Answer

the answer must be 2sqrt of 23 according to the book

anonymous · Answer

V=lwh = 192

wolf1728 · Answer

gonna go for a while

triciaal · Answer

@wolf1728 thanks

triciaal · Answer

ratio 2:3:4  l:w:h

triciaal · Answer

|dw:1431751937010:dw|


will the green line be the diameter of the sphere?   Can someone add the sphere please?