SOLUTION: Two rectangular prisms have the same volume. The area of the base of the blue prism is 2 1/6 square units. The area of the base of the red prism is one third that of the blue prism

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Question 1034896: Two rectangular prisms have the same volume. The area of the base of the blue prism is 2 1/6 square units. The area of the base of the red prism is one third that of the blue prism.
which stament is true?
a)The height of the red prism is one-third the height of the blue prism
B)The height of the red prism is the same as the height of the blue prism
C)The height of the red prism is six times the height of the blue prism.
D)The height of the red prism is three times the height of the blue prism.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
volume of the red prism = h1 * B1
volume of the blue prism = h2 * B2
area of the base of the red prism = 1/3 * the area of the base of the blue prism.
you get B2/3.
volume of the red prism = h1 * B2/3.
volume of the blue prism is still h2 * B2.
since the volumes are equal, you get:
h1 * B2/3 = h2 * B2
divide both sides of this equation by B2 and you get:
h1/3 = h2
multiply both sides of this equation by 3 and you get:
h1 = 3 * h2.
if the area of the base of the red prism is 1/3 * the area of the base of the blue prism, then the height of the red prism is 3 times the height of the blue prism.

this is easy to see if you use numbers.
any numbers will do.
assume the height of the blue prism is 6 and the area of the base of the blue prism is 9.
the volume of the blue prism is therefore 6*9 = 54.
now assume the area of the base of the red prism is 3.
that's 1/3 * 9.
in order for the volume to be the same, the height of the red prism has to be 3 * 6 = 18.
you get 18*3 = 54.
6*9 =54
18*3 = 54
18 is 3*6
3 is 9/3

your solution is selection D.