Molten metal is poured into the pouring cup of a sand mold at a steady rate of 400 cm3/s. the molten metal overflows from the pouring cup and flows into the downsprue. the cross section of the sprue is round, with a diameter at the top = 3.4 cm. if the sprue is 20 cm long, determine the proper diameter at its base so as to maintain the same volume flow rate.

The temperature in gavin's oven is a sinusoidal function of time. gavin sets his oven so that it has a maximum temperature of 280°f and a minimum temperature of 240°. once the temperature hits 280°, it takes 20 minutes before it is 280° again. gavin's cake needs to be in the oven for 30 minutes at temperatures at or above 270°. he puts the cake into the oven when it is at 260° and rising. how long will gavin need to leave the cake in the oven? (round your answer to the nearest minute.)