# Answer to Question #33394 in Geometry for richard

Question #33394

A coin has a mass of approx 10g, a new coin is minted and its size is doubled in all dimensions. What is the new coins mass?

Expert's answer

Acoin has a cylindrical form: it has radius R and height h.

So its volume is pi * R^2 * h and the mass is m = rho * V = rho * pi * R^2 * h,

where rho is the density of the coin.

Now suppose we doubled each dimension of the coin so the radius is 2R and

height is 2h.

Then the mass is rho * pi * (2R)^2 * (2h) = rho * 4 * R^2 * 2 * h = 8 * m = 8 *

10 = 80g.

So the mass of the new coin is 80 g.

So its volume is pi * R^2 * h and the mass is m = rho * V = rho * pi * R^2 * h,

where rho is the density of the coin.

Now suppose we doubled each dimension of the coin so the radius is 2R and

height is 2h.

Then the mass is rho * pi * (2R)^2 * (2h) = rho * 4 * R^2 * 2 * h = 8 * m = 8 *

10 = 80g.

So the mass of the new coin is 80 g.

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