Your roommate is a baking lover. She is baking a cake for your birthday. You are a curious person and decide to take a look at the cake while it is in the oven. When you take a look at your cake you realize three things. First, your roommate chose a rectangular prism cake tin. The base of the tin is a rectangle of size 20x30cm. The height of the tin is 10cm. However, the tin is only half full. Second, you see that due to the baking soda, the upper surface of the cake is going up at a rate of 0.5cm/min. Third, your roommate chose to prepare a chocolate cake. You want to know the rate at which the volume of the cake is changing when the tin is full.

The volume of a rectangular prism is given by:

V=Area of the base x height

Since the volume is changing only due to the change in height. the rate of change of the volume, by implicit differentiation, is given by:

dV/dt = (20cm) x (30cm) x dh/dt

dV/dt = 600cm x 0.5cm²/min

dV/dt = 300 cm³/min