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First, let's calculate the volume of the solid metal cylinder:
Radius of the cylinder (r) = 8cm / 2 = 4cm
Volume = πr^2h
Volume = π(4cm)^2 * 8cm
Volume = π * 16cm^2 * 8cm
Volume = 128Ï€ cm^3
Next, let's calculate the volume of each disc:
Radius of the disc (r) = 4cm / 2 = 2cm
Height of the disc (h) = 5mm = 0.5cm
Volume = πr^2h
Volume = π(2cm)^2 * 0.5cm
Volume = π * 4cm^2 * 0.5cm
Volume = 2Ï€ cm^3
Now, we can calculate how many discs can be made from the solid metal cylinder:
Number of discs = Volume of cylinder / Volume of each disc
Number of discs = 128Ï€ cm^3 / 2Ï€ cm^3
Number of discs = 64
Therefore, 64 discs can be made from the solid metal cylinder.