Ash R.

asked • 01/05/15

two similar cubes have sides 3cm and 6cm respectively. face area of the smaller cube is 8cm square, find the surface area or larger cube.

IGCSE mathematics. geometry

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Harvey F. answered • 01/05/15

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Hi Ash,
There is something wrong with the information in your question. A cube with a side of 3 cm has a face area of 9 cm2, not 8 cm2. Philip's advice using the scale factor is correct, but the answer you get may not agree with the true face area of a cube with a 6cm side. The true answer should be (6cm)2 since the area of a square is the square of a side length. You may want to give both answers when you turn in your assignment!
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Matt H.

I'm going to guess that the error is not in the numbers but in the use of the word "cube." I'd bet you're supposed to figure this with the dimensions given, as Philip did, but the proper term would be "rectangular prism."
 
 
The missing dimension in the smaller prism would measure 2.666... cm, so the corresponding dimension in the larger prism would be twice that, or 5.3333... cm, and therefore its face area would be 6 * 5.33333, or 32 cm squared.
 
To double check it, plug those numbers into the scale factor formula that Philip wrote out, and you'll see that it works!
 
All this goes to prove that we tutors should proofread every math book. :-)
 
 
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01/05/15

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