SOLUTION: A rectangular prism has sides that are in the ratio of 3:5:9. If the volume of the prism is 8640 cm^3, then what is the surface area of the prism in square millimeters?

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Question 1114544: A rectangular prism has sides that are in the ratio of 3:5:9. If the volume of the prism is 8640 cm^3, then what is the surface area of the prism in square millimeters?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let the dimensions be 3x, 5x, and 9x. Then the volume is

%283x%29%285x%29%289x%29=8640
135x%5E3+=+8640
x%5E3+=+64
x+=+4

The dimensions are 12, 20, and 36.

The surface area in cm^2 is
2%2812%2A20%2B12%2A36%2B20%2A36%29+=+2%281392%29+=+2784

A square cm is 100 square mm, so...

Answer: surface area is 278400 mm^2.