A 1 in diameter solid round bar has a groove 0.1 in deep with a 0.1 in radius machined into it. The bar is made of AISI 1040 CD steel and is subjected to purely reversed torque of 1800 lbf∙in. Determine the maximum shear stress taking the effect of the groove into account.

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.)