SOLUTION: The surface areas of 2 cubes are in the ratio of 64:25. If the length of one edge of the larger cube is 24 cm, what is the surface area of the smaller cube?

Algebra ->  Conversion and Units of Measurement -> SOLUTION: The surface areas of 2 cubes are in the ratio of 64:25. If the length of one edge of the larger cube is 24 cm, what is the surface area of the smaller cube?      Log On


   

Question 1027685: The surface areas of 2 cubes are in the ratio of 64:25. If the length of one edge of the larger cube is 24 cm, what is the surface area of the smaller cube?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the length of a side of
the smaller cube
+6s%5E2++ = the surface area of the smaller cube
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+25+%2F+64+=+%28+6s%5E2+%29+%2F+%28+6%2A24%5E2+%29+
+25+%2F+64+=++s%5E2+%2F+24%5E2+
+25%2F64+=+%28+s%2F24+%29%5E2+
Take the square root of both sides
+5%2F8+=+s%2F24+
Multiply both sides by +24+
+15+=+s+
This is the side of the smaller cube
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+6s%5E2+=+6%2A15%5E2+
+6s%5E2+=+6%2A225+
+6s%5E2+=+1350+
The surface area of the smaller cube is 1,350 cm2
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check:
+25%2F64+=+1350+%2F+%28+6%2A24%5E2+%29+
+25%2F64+=+1350+%2F+3456+
+.390625+=+.390625+
OK