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26 ••• Since 1983, the US Mint has coined pennies that are made out of zinc
with a copper cladding. The mass of this type of penny is 2.50 g. Model the penny
as a uniform cylinder of height 1.23 mm and radius 9.50 mm. Assume the copper
cladding is uniformly thick on all surfaces. If the density of zinc is 7140 kg/m3
and that of copper is 8930 kg/m3, what is the thickness of the copper cladding?
The problem is similar to a coin inside a coin. We need to find the outer coin's height- the inner coin's height or thickness of the outer coin.
The inner coin is made of Zinc.
m = (ρ Cu)Vcu + (ρ Zn) Vzn, where p is rho of Cu and Zn respectively and Vcu and Vzn are volumes of copper and zinc respectively.
m = ρ Cu[ 2π(r)square d + 2πr (h − 2d )d ] + ρ Zn π (r − d )(square) (h − 2d ), where d is the thickness sought.
Could someone help? I don't undestand why the V covering the zinc coin is, what's in bold.
The volume I get is total volume- volume of zinc coin: πr(square)h-π(r-d)(square)(h-2d)
with a copper cladding. The mass of this type of penny is 2.50 g. Model the penny
as a uniform cylinder of height 1.23 mm and radius 9.50 mm. Assume the copper
cladding is uniformly thick on all surfaces. If the density of zinc is 7140 kg/m3
and that of copper is 8930 kg/m3, what is the thickness of the copper cladding?
The problem is similar to a coin inside a coin. We need to find the outer coin's height- the inner coin's height or thickness of the outer coin.
The inner coin is made of Zinc.
m = (ρ Cu)Vcu + (ρ Zn) Vzn, where p is rho of Cu and Zn respectively and Vcu and Vzn are volumes of copper and zinc respectively.
m = ρ Cu[ 2π(r)square d + 2πr (h − 2d )d ] + ρ Zn π (r − d )(square) (h − 2d ), where d is the thickness sought.
Could someone help? I don't undestand why the V covering the zinc coin is, what's in bold.
The volume I get is total volume- volume of zinc coin: πr(square)h-π(r-d)(square)(h-2d)