Question 1034896
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.