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Maths question

I tried to do this question and i got an answer but i cant seem to find what the correct answer is anywhere can you tell me what you get.

Two solid plates P and Q are mathematically similar and made of the same material.
The surface area of P is p cm^2
The surface area of Q is q cm^2
The weight of P is w grams
Find an expression for the weight of Q.
Give answer in terms of p,q and w
Original post by someone1928
I tried to do this question and i got an answer but i cant seem to find what the correct answer is anywhere can you tell me what you get.

Two solid plates P and Q are mathematically similar and made of the same material.
The surface area of P is p cm^2
The surface area of Q is q cm^2
The weight of P is w grams
Find an expression for the weight of Q.
Give answer in terms of p,q and w


The area scale factor from P to Q is q/p, so the volume scale factor is (q/p)^(3/2). Now mass = density * volume, and as both P and Q are made of the same material, they both have the same density, so their mass is proportional to their volume, and thus the mass scale factor is the same as the volume scale factor, i.e. (q/p)^(3/2). Hence the mass of Q is w * the mass scale factor from P to Q, giving w(q/p)^(3/2).
(edited 5 years ago)

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