SOLUTION: The ratio of surface areas of two similar cubes is 25:64. Find the volume of the larger cube if the volume of the smaller cube is 1000in^3. A. 1600in^3 B. 2560in^3 C. 4096in^3

Question 740657: The ratio of surface areas of two similar cubes is 25:64. Find the volume of the larger cube if the volume of the smaller cube is 1000in^3.
A. 1600in^3
B. 2560in^3
C. 4096in^3
D. 6400in^3
I have answered B and been told it's incorrect.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The problem states that the ratio of surface areas of two similar cubes is 25:64. Find the volume of the larger cube if the volume of the smaller cube is 1000in^3.
The suface area of a cube is 6a*2, where a is the length of a side. Then,
25/64 = 6a^2 / 6b^2 and the ratio reduces to 5/8 = a/b
The volume of a cube is a^3 where a is the length of a side
For the smaller cube, we have
1000 = a^3 and a = 10
From our ratio we have 5/8 = 10/b and
5b = 80 and b = 16
16^3 = 4096 cubic inches which is the volume of the larger cube
therefore C is the correct choice
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