Paolo wants to surprise his girlfriend Jessica (who loves chocolate) by baking and decorating a cake for her to celebrate their anniversary. The frosting bag is in the shape of a right cone with a radius equal to its height. He squeezes the bag with constant pressure so that he applies $15$ cubic centimeters of frosting per minute.

1. How much frosting will Paolo have put on the cake after 42 seconds?

   Hint (a):

   We know that Paolo squeezes $15$ cubic centimeters of frosting every 60 seconds.

2. How fast is the radius of the frosting bag changing at the moment the radius is $1.7$ cm?

3. Will Jessica like the cake?

   Hint (c):

   What type of cake does Jessica like?