A thief uses a can of sand to replace a solid gold cylinder that sits on a weight-sensitive, alarmed pedestal. The can of sand and the gold cylinder have exactly the same dimensions (length = 23cm and radius = 3.9cm ).

Neat. Is there a question here?

To solve this problem, we need to determine the weight difference between the can of sand and the solid gold cylinder.

Step 1: Calculate the volume of the can and the solid gold cylinder.
The volume of a cylinder can be calculated using the formula: V = π * r^2 * h, where r is the radius and h is the height (length in this case).

For both the can of sand and the solid gold cylinder:
radius (r) = 3.9 cm
length (h) = 23 cm

Volume of the can (V_can) = π * (3.9)^2 * 23 = 3343.73 cm^3
Volume of the solid gold cylinder (V_gold) = π * (3.9)^2 * 23 = 3343.73 cm^3

Step 2: Calculate the weight difference between the can of sand and the solid gold cylinder.
The weight of an object can be calculated using its volume and density.

Density of gold (ρ_gold) = 19.3 g/cm^3 (approximate value for gold)

Weight of the can of sand (W_can) = V_can * ρ_sand
Weight of the solid gold cylinder (W_gold) = V_gold * ρ_gold

Step 3: Calculate the weight difference.
Weight difference = W_gold - W_can

Let's calculate the weight difference using the given dimensions and known density of gold:

Weight of the can of sand (W_can) = 3343.73 cm^3 * ρ_sand
Weight of the solid gold cylinder (W_gold) = 3343.73 cm^3 * 19.3 g/cm^3

Weight difference = W_gold - W_can

You would need to provide the density of the sand, or any other information related to the problem, in order to calculate the weight difference accurately.