Anyone up for correcting me :D?
Farah made two similar glass display boxes shaped like triangular prisms. The length of the sides of the base of the first display box is 3 feet, and the length of the sides of the base of the second display box is 6 feet. If the volume of the first display box is 32 ft3, what is the volume of the second display box?

Question

anonymous · Answer

i got 64ft^3

anonymous · Answer

I think, since the prisms are similar, all the dimensions are bigger, so the area of the base is four times as big, and the height is twice as big, so the volume is greater by a factor of eight.  That would give a volume of the larger prism of about 256 ft^3.

directrix · Answer

If two solids are similar, the ratio of their volumes is equal to the cube of their scale factor.
32/V = (3/6)^3 where V is the volume of the enlarged prism and (3/6) is the scale factor of the two similar solids.
32/V = (1/2)^3
32/V = 1/8
V = 256 cubic feet