A probe sent to the surface of Mars uncovers a pure platinum disc inscribed with the message, "We'll be right back" (in Martian, of course!). The disc is 3 inches thick and 0.4 meters in diameter. The density of platinum is 21,450 kg/m3. What is the mass of the platinum disc in pounds (lbm)?

Respuesta :

Answer:

Mass of  the disc in pounds is 45.288 lbm

Explanation:

Thickness of the disc [tex]t=3 inch=3\times 2.54=7.62 mm=7.62\times 10^{-3} m[/tex]

diameter of the disc [tex]d=0.4 m[/tex]

Density of the platinum [tex]\rho =21450 kg/m^3[/tex]

Volume of the disc

[tex]V=\frac{\pi d^2}{4} \times t\\V=\frac{\pi \times 0.4^2}{4} \times 7.62\times 10^{-3}\\V=9.57\times 10^{-4} m^3[/tex]

Mass of the disc

[tex]M=\rho \times V\\M=21450\times 9.5755 \times 10^{-4}\\M=20.539 kg[/tex]

Mass of  the disc in pounds is

[tex]M\times 2.205 =20.539\times 2.205=45.288 lbm[/tex]