SOLUTION: To study amoebae in pond water, a student completely filled two cube-shaped containers with samples of pond water. When filled, the first container held 27 cubic centimeters of

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Question 1195283: To study amoebae in pond water, a student completely filled two cube-shaped containers with samples of pond water. When filled, the first container held 27 cubic centimeters of pond water. The length of each side of the second container was twice the length of each side of the first container. How many cubic centimeters of pond water did the second container hold when filled?
Answer by ikleyn(52817) About Me  (Show Source):
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To study amoebae in pond water, a student completely filled two cube-shaped containers
with samples of pond water. When filled, the first container held 27 cubic centimeters
of pond water. The length of each side of the second container was twice the length
of each side of the first container. How many cubic centimeters of pond water
did the second container hold when filled?
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Since the volume of the first container is 27 cm^3, the edge of this cubic container
is  root%283%2C27%29 = 3 cm.


Then the edge of the second container is 2*3 = 6 cm.


Hence, the volume of the second container is  6*6*6 = 6%5E3 = 216 cm^3.    ANSWER

Solved. 

Another way to solve the problem is to notice that the second cube is geometrically similar to the first cube,
and the similarity coefficient is 2 (from larger to smaller cube).


It implies that the volume of the second cube is  2%5E3 = 8  times the volume of the smaller cube.


Thus  the volume of the second cube is  8*27 = 216 cm^3.