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

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.

RELATED QUESTIONS
Two rectangular prisms have the same volume. The area of the base of the blue prism is... (answered by Alan3354,ikleyn)

Two rectangular prisms each have a surface area of 600 square inches.what are some... (answered by ben720)

A pyramid and prism have the same base area and height. The prism's base area is 8 square (answered by Alan3354)

A rectangular prism has a base area of 400 square inches. The volume of the prism is 2 ,... (answered by KMST)

The scale factor of two similar rectangular prisms is 3. The surface area of the smaller (answered by fractalier)

If you are given two similar rectangular prisms with a ratio of 1:3 where the volume of... (answered by KMST)

My problem is to find the total surface area of a rectangular prism. The prisms... (answered by mananth)

draw a rectangular prism. The rectangular base has side lengths of 4 and 6 units. The... (answered by solver91311)

Draw two prisms, each with a base of area 40 square centimeters and a height of 5... (answered by richard1234)