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Consider a sphere of diameter 5 cm, a cube of side length 5 cm, and a rectangular prism of dimension 4 cm x 5 cm x 6 cm, all initially at 0 C and all made of silver (k=429 W/mK, rho=10500 kg/m^3, c_p=0.235 kJ/kgK). Now all three of these geometries are exposed to ambient air at 33 C on all of their surfaces with a heat transfer coefficient of 12 W/m^2 K. Determine how long it will take for the temperature of each geometry to rise to 25 C.

Consider a sphere of diameter 5 cm, a cube of side length 5 cm, and a rectangular prism of dimension 4 cm x 5 cm x 6 cm, all initially at 0 C and all made of silver (k=429 W/mK, rho=10500 kg/m^3, c_p=0.235 kJ/kgK). Now all three of these geometries are exposed to ambient air at 33 C on all of their surfaces with a heat transfer coefficient of 12 W/m^2 K. Determine how long it will take for the temperature of each geometry to rise to 25 C.